System, apparatus and method for the recording and projection of images in substantially 3-dimensional format

ABSTRACT

A system for the production of a second three-dimensional image magnified from a first three-dimensional image in substantially the same proportions, including a first active optical system for creating from the three-dimensional image, a first two-dimensional array. The array is comprised of two-dimensional elemental images. The first active optical system has a number of elements which is equal to the number of elemental images in the array. The configuration of the elements of the first active optical system corresponds to the configuration of the elemental images in the array. The first array is magnified equally in all directions to create a second two-dimensional array comprised also of two-dimensional elemental images. A second active optical system reconstructs a second three-dimensional image that is a magnification of the first three-dimensional image. The second active optical system has an F-number equal to the F-number of the first active optical system. The number of elements in the second active optical system is equal to the number of elemental images in the array. The configuration of the elements in the second active optical system corresponds to the configuration of the elemental images in the array. All of the component parts of an equation for determining the F-number of the second active optical system are the same multiples of all of the component parts used for determining the F-number of the first active optical system, respectively. The multiple is equal to the selected magnification factor.

CROSS-REFERENCE TO RELATED APPLICATION(S)

This application is a continuation of, and claims benefit of, U.S.Non-Provisional Application Ser. No. 09/111,990 filed Jul. 8, 1998, nowU.S. Pat. No. 6,229,562 which in turn claims the benefit of U.S.Provisional Application Ser. No. U.S. 60/051,972, filed Jul. 8, 1997.The foregoing applications are incorporated by reference in theirentirety herein.

FIELD OF THE INVENTION

This invention relates to method and apparatus for making and projectingthree-dimensional images recorded via the principles of holographyand/or integral photography.

BACKGROUND OF THE INVENTION

The artistic and photographic rendering of three-dimensional images isnot new. During the late nineteenth century, commercial stereoscopesbecame very popular toys and novelties. These devices employed theprinciple of stereoscopy. Most people see with two eyes. When a personopens only one eye, he sees a two-dimensional image of a life-scene froma particular view point. By using his eyes one at a time, he sees twodifferent two-dimensional images but from slightly different viewpoints. When both eyes are open, the individual's mind merges the twoimages and acquires depth information. Therefore, both eyes are neededto enable the mind to perceive a three-dimensional scene. The principleof stereoscopy tricks a person into perceiving depth by presenting eachof his eyes with separated pictures representing a given scene fromslightly different view points. If the distance between the view pointsis approximately equal to the distance between his eyes, he will see thescene in full three-dimensions.

Over the years, a number of stereoscopic devices were invented to enablepeople to view three-dimensional scenes. The first scenes werereconstructed from pairs of drawings of the same scene. The two drawingswere only slightly different, and were drawn as geometric projections ofthe same object or scene from a slightly different perspective.Eventually, stereoscopic cameras were invented that would producephotographs that would enable three-dimensional reconstruction of aphotographed scene. These cameras normally have two lenses situated adistance apart equal to the interoccular separation. The camera normallytakes two stereo paired photographs of the same scene with a singleexposure. When these photographs are developed and viewed with anappropriate viewing device, a three-dimensional picture is perceived.

First, people were able to purchase various types of stereoscopes forviewing these pictures. Then, during the earlier part of the twentiethcentury, lenticular stereograms became available. These are integratedphotographs (or drawings) for which no external viewing device isnecessary to be able to perceive a three dimensional image. A stereogramemploys a lenticular sheet comprised of small parallel cylindricallenses. This cylindrical lenticular sheet is often called a BonnetScreen. To prepare a stereogram, first a stereo pair of pictures areproduced of the scene. These stereo pairs are exposed separately, butfrom slightly different angles, on a photographic film through a BonnetScreen. After development, a viewer looking at the photograph through aBonnet Screen sees each of the two stereo pairs reconstructed at thesame angles at which they were exposed. Therefore, the twotwo-dimensional pictures are separated so that they are each seen by theviewer individually with each eye. Because of this, the viewer perceivesa three-dimensional scene. The lenticular stereogram was the firstdevice available wherein the stereo paired pictures were integrated intothe same frame. Photographs designed for viewing with a stereoscope areindividually viewable as two-dimensional pictures when the stereoscopeis not in use. However, the lenticular stereogram, when viewed withoutthe Bonnet Screen, is a very confusing picture.

Two additional processes were developed that integrated the stereopaired pictures into the same frame—the anaglyph and the vectograph. Theanaglyph permitted two black-and-white stereo paired pictures to beexposed on color film—one picture being exposed using a red filter andthe other exposed using a blue or green filter. When viewed with specialglasses, one lens being colored red and the other colored blue (orgreen), a three-dimensional scene is perceived. The vectograph permittedtwo stereo paired pictures to be exposed on a film with an emulsion onboth sides—one picture being exposed on one side of the film and theother picture being exposed on the other side of the film. The twopictures are developed such that light passing through one is polarizedin one direction while light passing through the other is polarized inthe other direction. This permits a viewer to use special glassesconsisting of Polaroid filters to see the three-dimensional scene.Vectography has the advantage over anaglyphic photography that avoidsthe annoyance of seeing the red-blue tint in the scene. Anaglyphic andvectographic slides (transparencies that could be viewed in a slideprojector) were widely sold. This resulted in an audience being able toview a magnified three-dimensional scene on a screen.

Eventually, anaglyphic motion pictures were displayed in theaters andultimately on television. They were never popular as audiences found thered-blue tints very annoying. The process was refined for television topermit viewing of full color movies in three-dimensions. However, use ofthe red and blue glasses still produced the annoying red-blue tint.Movies employing this process were broadcast on television as late asthe mid-1980's.

Vectography was never used in the cinema, but a process called “3-D” wasused to produce motion pictures. This process enjoyed reasonablepopularity during the 1950's. It employed a special projector with twolenses that projected each of the two stereo pairs onto an aluminizedscreen. Each stereo pair had a different polarity such that when aviewer used special Polaroid viewing glasses he would see a differentpicture with each eye. Since Polaroid filters are untinted, the 3-Dmovies could be viewed in full color. However, the popularity of 3-Dmovies eventually waned. The process is occasionally revived in presentday movies, but it remains unpopular. Audiences often experienced eyestrain and headaches while watching these films. They erroneously blamedthis on being required to wear special glasses.

Several attempts were made to create stereoscopic motion pictures thatcould be viewed as three-dimensional scenes without glasses. In 1969,Dennis Gabor, inventor of the hologram, developed a process wherein astereoscopic movie could be viewed by the unaided eye using a specialscreen. This process was never implemented. Had these movies beenproduced, the process would have required viewers to keep their heads inrelatively fixed positions.

It is interesting that most people blamed the eye strain and headachesresulting from viewing 3-D movies on the glasses. One-half of allAmericans wear glasses and are not bothered by them. However, the use ofglasses was the only thing that appeared different to audiences, andtherefore, must have caused the problem. However, the problem wasactually caused by a basic problem inherent in the process ofstereoscopy. When someone observes a real object, his eyes both convergeand focus on the object at the same time. However, when he observes astereo pair, his eyes converge on the apparent position of the objectbut focus on the screen or picture focal plane. A condition where one'seyes converge and focus at different positions is an unnatural viewingcondition. The result is eye strain. All stereoscopic processes havethis problem. It cannot be avoided.

Dennis Gabor invented the hologram in 1948, and in 1964, Emmet Leith andJuris Upatnicks made holography practical for the production ofthree-dimensional images. Holography produces three-dimensional imagesusing a principle different from stereoscopy. In order to understandwhat holography is, one must first understand the concept ofinterference. If a small pebble is thrown into a still pool of water,waves are generated, traveling as circles away from the point of origin.A second pebble thrown into the water will generate a new set of waves.When these two waves meet, a new wave pattern is set up in the water,resulting from the interference of the two original waves. Light is alsoa wave-like phenomenon. Two intersecting light beams will similarlyinterfere to generate a resulting wave pattern. Were the two light beamsto interact at the surface of a photographic plate, the interferencepattern would then be photographed. Such a photograph is called aninterferogram.

A hologram is a special type of interferogram. In order to produce ahologram, one of the interfering light waves must have an identifiablewavefront which can be easily reproduced or regenerated. This is calledthe reference beam. The second light wave is generally more complex, andis usually characteristic of the wavefront reflected from some object orscene. This is called the object beam. If, after the resultinginterferogram is developed, were it to be illuminated by a wavefrontidentical to the reference beam, the object wavefront would bereconstructed. In other words, were a viewer to look into the directionwhere the object was originally, he would observe the object wavefront.He would see the object before him in three-dimensions with such realitythat it would be impossible for him to determine visually whether or notthe object really exists. An interferogram of this type is called ahologram. The hologram is not a photograph of the object, but rather ofthe interference pattern containing all the information about theobject. It should be noted that no lenses need be used in makingholograms. Of course, more than one object beam can be used, and all ofthese wavefronts will be reconstructed simultaneously by a singlereference beam. Because the hologram is not a photograph of this scene,but rather a visual reconstruction of the objects in space as theyexisted at the time the hologram was taken, the viewer can observe thescene as he would were it to really exist. If one object blocks another,the viewer merely looks around it as he would ordinarily, and, behold,the hidden object becomes visible. Holography, therefore, provides astark reality that no other three-dimensional process can produce.

Integral photography is a photographic technique of producingthree-dimensional photographs by an integration process from manytwo-dimensional photographs each taken of the same object and event butat a slightly different viewing angle. In order to recreate thethree-dimensional effect from all these two-dimensional photographs, awavefront represented by the composite of all these elementalphotographs is reconstructed after development, and this wavefront issimilar to the wavefront produced by the three-dimensional scene itselfprovided that the integral photograph is viewed at a sufficient distanceaway. In fact, were the viewer to be positioned sufficiently far away asnot to be able to resolve the individual elements in the photograph(i.e., at minimum visual acuity), he would be unable to distinguish thewavefront reconstructed from the integral photograph from that producedby the actual scene. The viewer would observe the scene in truethree-dimensions. Unlike stereoscopic three-dimensionality, no specialdevice need by worn by the viewer, and the illusion of depth of thescene in integral photography does not have to be created in the mind ofthe viewer; the three-dimensional images actually exist in space. Ahologram is a photograph which is capable of reconstructing the samewavefront as would be created by the actual scene. In fact, were thehologram to be properly illuminated, it would not be possible for theviewer to perform any visual test to determine whether or not theobjects in the scene were real. Were one to view the hologram through asmall aperture, the entire scene would be visible. Moving the aperturearound only changes the viewing angle. No matter how small the apertureis (within reason—limited by a size somewhat larger than the grain ofthe film) the entire scene would still be visible. A hologram can, then,be thought of as an integral photograph whose elemental photographs areof infinitesimal size. Therefore, an integral photograph can be thoughof as being equivalent to a hologram when the viewer is positioned atminimum visual acuity.

Projection of magnified three-dimensional scenes from holograms orintegral photographs before large audiences has never been implemented.First, if one were to project a hologram onto a conventional screen, noimage of the scene would be produced. Since a hologram is a photographthat contains information about an object and not of the object itself,a hologram projected onto a screen as a magnified photograph would notbe seen as anything meaningful. On the other hand, if one were toproduce a large magnified hologram so as to enable viewing before alarge audience, the principles of holography dictate that thereconstructed three-dimensional image would be de-magnified. Second,there is a basic principle governing the magnification ofthree-dimensional images. If the three-dimensional image itself were tobe magnified, the magnification in depth would be equal to the square ofthe lateral magnification. Such an image would not be viewable as anatural three-dimensional object. Finally, a number of engineeringdifficulties exist in the current state-of-the-art that have madeprojection of magnified three-dimensional scenes before large audiencesimpractical.

In view of the above, it is therefore an object of the invention toprovide a three-dimensional system and method in which non-stereoscopicimages can be magnified and projected before large audiences. Anotherobject of the invention is to provide such system wherein said imagesare still life pictures and/or moving pictures. Yet another object ofthe invention is to provide a three-dimensional system which isadaptable for use in animation, home entertainment and computertechnology.

SUMMARY OF THE INVENTION

These and other objects of the invention which shall be hereinafterapparent are achieved by the SYSTEM AND APPARATUS FOR THE RECORDING ANDPROJECTION OF IMAGES IN SUBSTANTIALLY 3-DIMENSIONAL FORMAT comprising amethod and apparatus for reducing a three-dimensional scene to anintegral photograph and thereafter magnifying the integral photograph aswell as the optics used to create the integral photograph by the samescaling factor so as to project a magnified three-dimensional image. Theinvention comprises a camera for photographing the scene, a projectorfor reconstructing the scene in three-dimensions, a screen which is anactive optical element in the process and a method of editing motionpicture film used in this process. The invention also includes a methodand apparatus for fabricating holograms of live three-dimensionalscenes, for projecting magnified three-dimensional images produced fromthese holograms before large audiences, and for editing motion picturefilm. This invention provides a system which is adaptable to animation,home entertainment and computer technology.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be better understood by the Detailed Description ofthe Preferred and Alternate Embodiments with reference to the drawings,in which:

FIG. 1 illustrates the method of magnification that is the basis forthis application.

FIG. 2 illustrates how a magnified image can be projected before anaudience.

FIG. 3 illustrates the appearance of a two-dimensional integralphotograph projected upon a screen using the preferred embodiment ofthis invention.

FIG. 4 shows how the integral photograph shown in FIG. 3 can bemultiplexed onto a rectangular film format. FIG. 4(a) shows the formatof the original integral photograph. FIG. 4(b) shows the format of themultiplexed film.

FIG. 5 is a schematic of the preferred embodiment of the camera.

FIG. 6 is a drawing showing a fiber optics image dissector andmultiplexer.

FIG. 7 shows the design considerations for the camera matrix lens array.

FIG. 8 shows the parameters for the determination of acceptance angle.

FIG. 9 is a drawing showing a matrix lens array consisting of smallspherical lenslets that are hexagonally close-packed.

FIG. 10 is a drawing showing a matrix lens array consisting of a squarearray of small criss-crossed cylindrical lenslets.

FIG. 11 is a schematic of a Fresnel Zone Plate.

FIG. 12 is a schematic of a Gabor Zone Plate.

FIG. 13 is a schematic of a Holographic Zone Plate.

FIG. 14 is a schematic of a zone plate matrix lens array optical system.

FIG. 15 is a schematic of a zone plate matrix lens array optical systemwhere vertical parallax has been eliminated.

FIG. 16 is a schematic showing the abberations caused by a cylindricallens.

FIG. 17 shows lenslet resolution limitations due to abberation.

FIG. 18 is a schematic of a zone plate matrix lens array optical systemwhere vertical parallax has been eliminated and correction has been madefor abberations.

FIG. 19 is a schematic of a multistage camera.

FIG. 20 is a schematic of holographic multiplexing optics.

FIG. 21 is a schematic showing the method of holographic multiplexingusing the optics shown in FIG. 20.

FIG. 22 is a schematic showing the conventions used in describing axesof rotation.

FIG. 23 is an optical ray trace to aid in an optical evaluation of theregistration problem.

FIG. 24 represents three drawings showing a solution to the registrationproblem. FIG. 24(a) shows the three-point film registration system. FIG.24(b) shows how the film registration holes can be formed. FIG. 24(c)shows how the film is registered during photography and projection.

FIG. 25 shows the different types of three-dimensional images that canbe projected for viewing by a theater audience.

FIG. 26 are optical ray traces showing the different types ofthree-dimensional images that can be projected for viewing by a theateraudience. FIG. 26(a) shows the projection of a real image that is largerthan the screen. FIG. 26(b) shows the projection of a real image that issmaller than the screen. FIG. 26(c) shows the projection of virtualimages both smaller and larger than the screen.

FIG. 27 shows the acceptance angle limitation on audience size.

FIG. 28 shows the flipping limitation on audience size.

FIG. 29 shows geometric parameters used for computation of limitationson audience size.

FIG. 30 shows the process for formation or manufacture of the frontprojection holographic screen.

FIG. 31 shows the method of reconstruction from projection onto thefront projection holographic screen.

FIG. 32 shows a screen consisting of hexagonally close-packed sphericallenslets.

FIG. 33 shows a screen consisting of crossed cylindrical lenslets.

FIG. 34 shows a screen consisting of reflective concave lenslets (a) andcorner cubes (b).

FIG. 35 shows a projection from a reflective cylindrical frontprojection screen.

FIG. 36 shows a circular zone plate screen.

FIG. 37 shows a cylindrical zone plate screen.

FIG. 38 shows a cylindrical lenticular screen.

FIG. 39 is a schematic showing the separation of multiplexed images.

FIG. 40 is an optical ray trace used for the design of projectionoptics.

FIG. 41 is a schematic showing the basic principle of primaryholographic projection.

FIG. 42 is a schematic showing projection of a real image from ahologram.

FIG. 43 is a schematic of a primary holographic imaging system usinghigh quality optics.

FIG. 44(a) is a schematic of primary projection using a high qualityholographic lens. FIG. 44(b) shows a method of making the holographictens described in FIG. 44(a).

FIG. 45 is a schematic of primary holographic projection using a matrixlens array.

FIG. 46 is a schematic of primary holographic projection using twomatrix lens arrays.

FIG. 47 shows the method of fabricating a fiber optics magnifier.

FIG. 48 illustrates primary magnification using fiber optics.

FIG. 49 shows the steps that must be accomplished during theunmultiplexing process.

FIG. 50 is a drawing of an unmultiplexing prism.

FIG. 51 is a schematic showing unmultiplexing using a holographicimaging device.

FIG. 52 is a schematic showing the standard method of image inversion.

FIG. 53 shows how image inversion can be accomplished without loss ofresolution.

FIG. 54 is a schematic showing the optics of the preferred embodiment ofthe holographic projector.

FIGS. 55(a) and (b) are optical ray traces used for the design of thelenses for final projection.

FIG. 56 is a schematic and optical ray trace for an anamorphic lens.

FIG. 57 is a shcmatic showing two types of carbon arc lamps.

FIG. 58(a) is an optical ray trace of misregistration of virtual imagesdue to vibration. FIGS. 58(b), (c) and (d) are geometric figures neededfor misregistration calculations.

FIG. 59(a) is a schematic showing magnification of a reconstructed realthree-dimensional image from a hologram FIG. 59(b) is a schematicshowing magnification of a reconstructed three-dimensional virtual imagefrom a hologram.

FIG. 60(a) is a schematic showing projection of a two-dimensional imagefrom a hologram.

FIG. 60(b) is a schematic showing projection of an integral photographfrom a three-dimensional hologram.

FIG. 61(a) is an optical ray trace and schematic showing the workings ofa birefringent crystal. FIG. 61(b) is a schematic showing a method ofobtaining parallel beams from one beam using birefringent crystals. FIG.61(c) is a drawing of a wedge plate. FIG. 61(d) is an optical ray traceand schematic showing how a wedge plate can be used to project anintegral photograph.

FIG. 62 shows the use of a hologram whose reconstructed real image is atwo-dimensional integral photograph.

FIG. 63(a) shows a method of taking composite photographs. FIGS. 63(b)and (c) are schematics showing how the elemental photographs produced bythe method of FIG. 63(a) can be converted to a hologram FIG. 63(d) showsa method of taking elemental photographs. FIG. 63(e) shows a method ofsynthesis of a hologram on a high resolution photographic plate done insequence on the same plate when an aperture is moved. FIG. 63(f) showsthe holographic wavefront reconstruction of a pseudoscopic real image.

FIG. 64 shows a method of preparing strip holograms.

FIG. 65 shows image inversion from pseudoscopy to orthoscopy usingintegral photography.

FIG. 66 shows image inversion from pseudoscopy to orthoscopy usingholography and integral photography.

FIG. 67 shows image inversion from pseudoscopy to orthoscopy usingholography.

FIG. 68 shows image inversion from pseudoscopy to orthoscopy by elementreversal.

FIG. 69 shows the principles of a holographic printing press.

FIG. 70(a) shows an editor for integral photographic film. FIG. 70(b)shows an editor for holographic film.

DETAILED DESCRIPTION OF THE PREFERRED AND ALTERNATE EMBODIMENTS

The present invention, in all its embodiments, is based upon a methodthat permits magnification of a three-dimensional image produced from aphotograph, hologram, optical system or other system or device,regardless of the medium or the method, in such manner as to preservethe depth to height and width relationship of the image as it existedprior to magnification. This method requires the three-dimensional imageprior to magnification to be rendered as an array of two-dimensionalimages by some form of matrix lens array, such as a fly's eye lens. Werethis array of two-dimensional images to be magnified by somemagnification factor, and then viewed or projected through a new matrixlens array that has been scaled up from the lens array that produced theoriginal array of two-dimensional images, such that the scaling factoris equal to the magnification (i.e., the focal length and diameter ofeach lenslet must be multiplied by the same magnification factor), a newthree-dimensional image would be produced that would be magnified by thesame magnification factor, and all image dimensions would be magnifiedby the same factor such that all dimensions of the finalthree-dimensional image would be proportional to the dimensions of theoriginal image. The utility of magnifying three-dimensional images usingthis method would be the ability to enlarge holograms or integralphotographs or other media from which three-dimensional images areproduced, or to project still or moving three-dimensional images beforea large audience.

The magnification principle is illustrated in FIG. 1. Object 1 isphotographed by matrix lens array 2, thereby producing integralphotograph 3. Integral photograph 3 is then magnified to give integralphotograph 4 which is then placed behind matrix lens array 5. Thiscombination yields magnified image 6. It must be noted here, that duringscaling-up, the (F/#) of the lenslets remains constant.

Projection is merely another form of magnification. The only differencelies in the fact that no permanent record is produced as in photography.To illustrate the principle of projection, let us use as an example, thetechnique of rear projection shown in FIG. 2. (As will be seen later, itis also possible to illustrate this principle with front projection.)Were an integral photographic transparency to be projected at some givenmagnification onto a translucent screen 7 which is behind a large matrixlens array 8, an observer 9 in the audience sitting in front of thematrix lens array will see the magnified three-dimensional image 10. Thethree-dimensional image can be made orthoscopic, and can be made toappear either in front of or behind the matrix lens array. This will bediscussed later.

What requires description is the optical and mechanical system needed toproduce the initial two-dimensional array from the unmagnifiedthree-dimensional image (i.e., the camera), the optical and mechanicalsystem needed to produce the magnified three-dimensional image (i.e.,the projector), any intermediate medium needed to produce the magnifiedthree-dimensional image (i.e., the screen and/or any intermediateoptical system), and any devices that may be required for editing thetwo-dimensional images used to produce the three-dimensional image. Alsorequired is a description of the methods of photographing, projectingand editing magnified three-dimensional images.

The camera consists of an optical system that would produce thetwo-dimensional array of two-dimensional images on a plane, the planeand/or recording medium whereon the two-dimensional array is produced,the mechanical apparatus (if any) associated with the image plane and/orrecording medium, a means (if any) for adjusting the optical system forfocus and/or special effects, and the housing (if any) that integratesthe optical system, the mechanical system and the image plane and/orrecording medium into a single unit. An example of the optical system isa matrix lens array such as a fly's eye lens arranged so as to produce arectangular matrix array of rectangular two-dimensional images. Theimage plane, for example, would contain a film for recording thetwo-dimensional images. Once developed, the matrix array photographwould be called an integral photograph. If the camera is a motionpicture camera capable of capturing moving three-dimensional images inthe form of a sequential series of integral photographs, a film motionmechanism would be required. Finally, such a camera might require ahousing to integrate the components and to provide a dark environment soas to not expose the film unnecessarily.

In the preferred embodiment of this invention, three-dimensional imageswill be projected in a theater. Studies have indicated a desiredaudience viewing distance of from two to six times screen width. Thus,audience size and location can help determine acceptable screen size.Although many cinemas currently place their audiences closer to thescreen than twice the screen width, those spectators sitting this closeto the screen view even the present two-dimensional picturesuncomfortably. Insofar as theater and screen designs are concerned, thefollowing boundary conditions apply:

(1) To maximize the audience size, the (F/#) of both camera and screenlenslets must be chosen as low as possible. The upper limit on the (F/#)should be approximately 2.0, although slightly more can be tolerated,and one should try to achieve as close to an (F/#) of 1.0 or below aspossible. This is due to the acceptance angle and flipping limitationson audience size. These limitations will be discussed later.

(2) The number of elements in the matrix lens array of the camera mustequal the number of elements in the screen. Since there is a minimumsize that each lenslet in the camera lens array can practically be, anextraordinarily high number of elements will make utilization of thematrix lens array for normal motion picture photography veryimpractical. Since the size of each element, and, therefore, the numberof elements in the screen are determined by the viewing distance, thiswould impose severe limitations on camera design. A viewing distance ofapproximately twice the width of the screen seems to be practical,although this figure can be slightly adjusted.

Given the above two boundary conditions, the number of elements on thescreen may be determined as follows:

φ_(S)=2.91×10⁻⁴ S

n _(LINEAR) =w/φ _(S),

therefore,

n _(LINEAR)=3.46×10³(W/S)  [1]

where:

φ_(S)=the angle of minimum visual acuity

w=the width of a frame of film

n_(LINEAR)=the number of elements of minimum size that can be placed ina given width in one direction on the film or screen

W=the width of the screen

S=the minimum distance of a viewer from the screen

If (S/W)=2, then the screen and the camera will have 1,730 elements inthe W or horizontal direction. Convention has it today that the width ofa movie theater screen is twice its height. Therefore, the screen andcamera will have 865 elements in the height direction.

n _(TOTAL)=1.496×10⁶ elements

Considering a square array of elements on the film, since there are1,730 such elemental photographs in the horizontal direction, each suchelemental photograph will have a linear dimension of 5.78×10⁻⁴ w (wherew is the width of the frame). If we use conventional 70 mm film, thewidth of the frame is 65 mm, and, therefore, the linear dimension ofeach elemental photograph would be 0.0375 mm. Even were a filmresolution of 2,000 lines/mm to be used (this is the resolution of KODAKEmulsion 649-F which has an ASA Rating of 0.003), each picture wouldhave the total information given by 75 line pairs. However, elementallens resolution cannot be made better than 500 lines/mm. This reducesthe total available information for each picture to approximately 19line pairs. Furthermore, the ASA rating of this high resolution film isso small as to make using this film highly impractical. For bestresults, the film resolution should be approximately matched to thelenslet resolution, which, in this case is between 400-500 lines/mm.Even this is high resolution black & white film, but it is useable.

If we try to match the element size to that which would give areasonable elemental resolution, one must look for a total informationcapacity of approximately 400-500 line pairs, (possessing the imagequality of a commercial television picture). This would require lensletsone-mm square. The size of the film frame will be 1.73 meters×0.865meters. That is ridiculous! Even were the lenslets to be 0.4 mm, theframe would be 69.2 cm×34.6 cm, and with 0.1 mm lenslets (a situation ofunacceptable resolution) the frame size would be 173 mm×86.5 mm. Evenfilm of this size is impractically large. While it is true thatextremely small lenses and very high resolution film can produce a framesize which just enters the field of usability, the image resolution isso poor that the popularity of such a three-dimensional process would bein question.

A solution is available that avoids the problems of resolution; that isthe elimination of vertical parallax, the use of black-and-white filmfor color photography, and the use of elemental multiplexing on thefilm. This is the preferred embodiment of the camera. Theoretically, anintegral photograph produced by this type of camera will appear as shownin FIG. 3. The entire two-dimensional projected image 11 would consistof a multiplicity of two-dimensional elements 12. A projected integralphotograph with only horizontal parallax would look to be exactly thesame as the “lenticular” three-dimensional pictures currently on themarket. Vertical parallax would be missing, but horizontal parallaxwould be present. In normal use of stereoscopic vision, verticalparallax is not used, and horizontal parallax alone is sufficient togive a true three-dimensional effect. Since vertical parallax is notneeded for three-dimensional photography, horizontal elements can bemultiplexed vertically on the film. This is illustrated in FIG. 4. FIG.4(a) shows the original integral photograph with the elements arrangedhorizontally. FIG. 4(b) shows how the same elements can be arranged in arectangular format on the film.

It is highly desirable to use a practical commercial film with thehighest possible resolution. (It is extremely important that the maximumamount of information be recorded on each elemental photograph. This isdetermined not only by the lenslet characteristics but also by the filmresolution.) Unfortunately, color films are not commonly manufacturedwith the high resolution available from black-and-white films. For bestresults in reconstructing a sharp three-dimensional picture, highresolution black-and-white film should be used. However, color picturesare essential if the process described herein is to be commerciallysuccessful.

If the camera matrix lens array is designed to be used with a colorfilter plate (having red, blue and green elements alternating), eachelemental photograph of the integral photograph will possess thecharacteristics of having been photographed by monochromatic light(alternating red, blue and green). If black-and-white film were to beused in such a camera, and the final projected integral photograph bepassed through a color filter plate, such that the red color is added toeach elemental photograph taken using a red filter, blue color added tothose taken using a blue filter, and green color added to those takenusing a green filter, then the final projected picture will appear infull natural color, provided that the audience is far enough back fromthe screen that the individual elements cannot be resolved. (Colorplates can be used for this purpose even where integral photography isnot used. Such a color plate can be used in any conventional camera withblack-and-white film, and, as long as a second appropriate color plateis used for projection, color pictures can be obtained.).

FIG. 5 illustrates the basic concept of a camera which would do this. Instage 1 of the camera, the scene is first compressed in the verticaldirection by a cylindrical lens 13, but no focusing occurs in thehorizontal direction. Only when this vertically compressed pictureimpinges on the Bonnet lens 14 (with its associated color plate 15) isit focused in the horizontal direction to the correct number ofelemental photographs (horizontal) which have been foreshortened in thevertical direction as shown in FIG. 4(a). Stage 2 of the camera divertssections of this horizontal line of pictures onto different verticalpositions on As shown in FIG. 5, a two-dimensional image 18 of the typeshown in FIG. 4(a) is focused onto an image plane consisting of a fiberoptics face plate 16. The image is then transformed using a fiber opticsimage dissector and multiplexer 17. This optical device transforms atwo-dimensional image of the type shown in FIG. 4(a) impinging upon oneof its two image planes to a two-dimensional image of the type shown inFIG. 4(b) upon its second image plane. This transformed image is exposedon the film 18 which is in contact with the second image plane of device17. The method of performing the multiplexing is also shown in FIG. 6.The fiber optics image dissector and mutiplexer 17 serves to divertsections of the picture on image plane 16 to different positions on thefilm 18. The usual purpose of such a device is to act as a shapetransducer to increase the resolution of a television camera. Itconsists of several fiber optics sections, each section transmitting anddirecting the image with which it is in contact through the opticalfibers to a different position relative to the image in contact with anadjacent section. FIG. 6 shows this function being performed using animage orthocon tube. However, such fiber optics image dissectors can beconstructed to convert a strip image to a rectangular image on a film.Similarly, such a device can convert a multiplexed integral photographrectangular image on a film to a strip image for projection onto ascreen. A fiber optics device of this type is quite standard, althoughit would need to be constructed to provide the particular format whichwill be decided upon. Each transmitting section would have thedimensions 65 mm×δ, and 2-micron fibers would be used, separated by½-micron. Such a fiber optics device would provide a resolution of 400lines/mm. This device would be manufactured from rigid fibers and wouldnot be flexible. The adhesive which bonds the fibers together would beopaque, and, therefore, no crosstalk between fibers would occur.

The configuration of the matrix lens array of the camera is such that itwill be a long strip of lenslets. Immediately, this eliminates the useof a hand held camera. For most practical applications, the matrix lensarray will be between 1 and 2 meters long. Certainly, both structuralconsiderations and the difficulties in fabricating the multiplexingimage dissector prohibit the lens from being much larger than this. Evenwith this size lens, the camera must be moved with a dolly (a techniquewhich is quite standard in motion picture technology). Much largermatrix lens arrays would have to be held stationary. Although thisoption is not really practical, were camera motion to be eliminated,much larger matrix lens arrays could be used.

In terms of its mechanical stability, the matrix lens array must bestructurally braced so that no relative motion occurs between thelenslets, and so that no relative motion occurs between the matrix lensarray and the image plane.

To playback the system described above, one need merely reverse theoptics for projection; i.e., a highly anamorphic lens (for the verticaldirection) must be used to project this frame onto a special screen.

The screen is a set of vertical cylindrical lenses arrangedhorizontally, similar to what is used for the lenticularthree-dimensional process, along with a color plate if necessary.Instead of cylindrical lenses, vertical cylindrical zone plates (stampedor photographed or made by holography) or reflective optics can be used.The magnification principle still applies as has been previouslydescribed, but only in the horizontal direction. This will be discussedfurther.

To Perform a Typical Resolution Problem

Assume the audience will be seated at a minimum distance of twice thewidth of the screen. This requires 1,730 elements in the horizontaldirection. Using the method of elimination of vertical parallax, theseelements are cylindrical, and run along the entire height of the screen,i.e., only one element exists in the vertical direction. Assume thateach Bonnet element is 1 mm diameter, with a resolution of 500 lines permm. Therefore, the size of the Bonnet Lens Array is 1.73 metershorizontally×0.865 meters vertically. This will produce 1,730 individualelemental photographs. The size of the frame on 70 mm film is 65 mmhorizontally×32.5 mm vertically. This means that 65 individual picturescan fit on one row of the frame. This requires approximately 27 verticalrows to produce the 1,730 pictures. Therefore, each element isapproximately 1 mm×2.5 mm for a square format or 5 mm if the height ofthe frame is twice the width. The latter format is possible providedthat the film moves twice as fast. This is feasible. 1 mm elementsprovide sufficient resolution in the horizontal direction. This isfurther enhanced by the redundancy factor (which will be discussedlater) which will make the vertical resolution sufficient forcomfortable viewing.

FIGS. 7(a) through (e) are to be used for the camera lens designcomputations. FIG. 7(a) shows a section of the camera matrix lens array.It consists of a Bonnet Screen 20 consisting of 1,730 plano-convexvertical cylindrical lenses 19 arranged in the horizontal directioncrossed with one plano-convex cylindrical lens 21 in the horizontaldirection. FIG. 7(b) shows a horizontal section of the matrix lensarray. The parameters illustrated in this figure are arranged forcomputation in FIG. 7(c). FIG. 7(d) shows a vertical section of thematrix lens array, and its parameters are arranged for computation inFIG. 7(e).

Integral photography imposes a severe limitation on theater design,i.e., the total angle under which a spectator sitting on theperpendicular bisector of the screen views the three-dimensional virtualimage cannot be greater than the acceptance angle, ω, of each individuallenslet in the matrix lens array (as will be seen later, holography doesnot impose this limitation). The parameters for the determination ofthis acceptance angle are shown in FIG. 8. $\begin{matrix}{{\tan \quad \frac{\omega}{2}} = {\frac{\varphi \quad c}{2f_{c}} = \frac{1}{2\left( {F/\#} \right)}}} & \lbrack 2\rbrack\end{matrix}$

where:

ω=the acceptance angle

φ_(C)=the diameter of a single lenslet

ƒ_(C)=the focal length of a single lenslet

From equation 2, for each lens 19 in the Bonnet Screen 20, we have:$\begin{matrix}{\frac{\varphi}{2f} = {\tan \quad \frac{\omega}{2}}} & \lbrack 3\rbrack\end{matrix}$

and, similarly, for the crossed cylindrical element 21, we have:$\begin{matrix}{\frac{\delta}{2f} = {\tan \quad \frac{\psi}{2}}} & \lbrack 4\rbrack\end{matrix}$

where δ is the height of the lens (equivalent to the diameter of aspherical lens), ƒ is the focal length, and ψ is the cylindrical lensacceptance angle. From FIG. 7(c), we can see that:$\frac{x}{d} = {\tan \quad {\frac{\omega}{2}.}}$

Substituting into equation 3, we have $\begin{matrix}{{x = \frac{d\quad \varphi}{2f}},\quad {and}} & \lbrack 5\rbrack \\{w = {\varphi \left( {n + \frac{d}{f}} \right)}} & \lbrack 6\rbrack\end{matrix}$

From FIG. 7(e), we can see$\frac{x^{\prime}}{d} = {\tan \quad \frac{\psi}{2}}$

and, similarly, substitution into equation 4 yields$x^{\prime} = {\frac{d\quad \delta}{2f}.}$

Now, the total height of the frame at d is W/2. So, once again, fromFIG. 7(e), we have$\frac{W}{2} = {\delta \left( {1 + \frac{d}{f}} \right)}$

Substituting this expression into equation 6, we obtain${\delta \left( {1 + \frac{d}{f}} \right)} = {\frac{\varphi}{2}\left( {n + \frac{d}{f}} \right)}$

which yields: $\begin{matrix}{f = \frac{2d\quad \delta}{{\varphi \quad \left( {n + d} \right)} - {2\quad \delta}}} & \lbrack 7\rbrack\end{matrix}$

A more useful form of this equation is: $\begin{matrix}{d = \frac{{n\quad \varphi \quad {ff}} - {2{ff}}}{{2f} - {f\quad \varphi}}} & \lbrack 8\rbrack\end{matrix}$

where d represents the distance from the camera lens to an imaginaryframe or aperture whose width is twice its height and through which thescene would be seen in the same size and perspective as were the imagefrom the film to be projected onto a small screen of the same size(W×W/2) at that same distance d. As can be seen from equation 8, while dis dependent on both the diameter and focal length of each lenslet inthe Bonnet Screen, it is also dependent on the (F/#) of the crosscylindrical element.

The following procedure should be used for the camera lens design.First, select φ, n, and the size of the film frame. δ is thusdetermined. Then select the (F/#) of the lenslets in the Bonnet Screenportion of the lens and ƒ is determined. Select the (F/#) of thecylindrical element of the lens, and f is determined. Now, from the lensmaker's formula:$\frac{1}{F.L.} = {\left( {\eta - 1} \right)\quad {\left( {\frac{1}{r_{1}} - \frac{1}{r_{2}}} \right).}}$

For the cylindrical element of the lens which is plano-convex, either r₁or r₂ is infinite.

r=ƒ(η−1)  [9]

where r is the radius of the cylindrical element, and η is therefractive index of the lens material. Then:

2r≧δ  [10]

(The relationship 2r=δ will hold true only when the (F/#) of thecylindrical lens is 1.)

Now, let us show some examples:

Let (F/#)₁ be that of the Bonnet lenslet and (F/#)₂ be that of thecrossed cylindrical element. In this case, select a film frame size of65 mm×130 mm. Also, η is assumed to be 1.52.

TABLE 1 η φ, mm (F/#)₁ f, mm δ, mm (F/#)₂ f, mm r, mm d, mm W, mm 1,7341.2 1.7 2.04 4.06 1.7 6.91 3.59 3,530 4,150 1,707 0.8 1.7 1.36 6.18 1.710.53 5.39 2,330 2,733 1,707 0.8 1.7 1.36 6.18 1.2 7.42 3.81 1,285 2,1221,756 1.0 1.7 1.70 4.81 1.2 5.58 3.00 1,626 2,687 1,734 1.2 1.7 2.044.06 1.2 4.88 5.08 1,776 2,970

The results shown in Table 1 show that it is very important to make(F/#)₂ as small as possible. The figure of F/1.2 for the cylindricallens seems possible, as is shown by the figures for r. When (F/#)₂ ismade small, φ can be made somewhat larger without increasing d and W bytoo much. In such a case, there is a trade-off between horizontal andvertical resolution. d should be kept as low as possible, since anyobject coming closer to the camera than the distance d will appear infront of the screen after projection. A value for d ranging between 1and 2 seems optimum.

The design of the camera discussed above would apply to taking stillpictures or moving pictures. Clearly, in order to use this camera toproduce three-dimensional motion picture films, a film motion mechanismis required. However, before discussing the film motion mechanism, somealternate embodiments of camera design will be presented.

There are several alternatives for the matrix lens array used to createthe two-dimensional array of elemental pictures. One such alternative isan array of small spherical lenslets that are hexagonally close-packed.A matrix lens array of this type has often been referred to as a“fly's-eye lens.” These lens arrays are usually formed by pouring moltenglass or plastic into a mold. The mold is usually made by pressing smallmetal spheres into a copper master. In this case, the small spheres arearranged so that the maximum number can be contained in the smallestpossible space. This is done to eliminate as much dead space aspossible. Therefore, the spherical lenslets are hexagonally closepacked. Such a matrix lens array is shown in FIG. 9. The matrix lensarray 22 consists of many small spherical lenslets 23, each lensletbeing surrounded by six identical lenslets. This close packing patternof the lenslets is duplicated by the arrangement of the two-dimensionalelemental pictures on the film. Each elemental picture on the film mustalso be surrounded by six elemental pictures.

A second alternative for the matrix lens array would be a square arrayof small criss-crossed cylindrical lenslets. This array provides theclosest possible packing of lenslets with the complete elimination ofdead space. This is highly desirable. Equivalent spherical lenslets areproduced by crossing two sheets of cylindrical lenses and mating themorthogonal to each other. These cylindrical lens sheets, individually,are often called “lenticular lens sheets” or Bonnet Screens. Obviously,the focal lengths of the lenslets in the two arrays must be differentand computed so that they each focus on the image plane. Such a matrixlens array is shown in FIG. 10. FIG. 10(a) is a top view of the devicewhile FIGS. 10(b) and 10(c) represent side and front views respectively.This device 24 consists of two matrix lens arrays of the type describedas element 14 of FIG. 5. Each of these two matrix lens arrays arecomprised of small cylindrical lenslets 25. When the two arrays arecrossed such that the axes of the cylindrical lenslets on the arrays areorthogonal or perpendicular to each other, a two-dimensional array oftwo-dimensional elemental pictures can be produced.

A third alternative for the matrix lens array would be an arrangement ofzone plates. These are less commonly used devices for focusingelectromagnetic radiation. It has been used to focus radiation rangingfrom the infrared down to the soft X-Ray region. A Fresnel Zone Plateconsists essentially of concentric alternately opaque and transparentrings. A Fresnel Zone Plate can either be produced photographically, orby carving, etching, or stamping the zones in plastic or glass. The FZPis shown schematically in FIG. 11. FIG. 11(a) shows the appearance ofthe Fresnel Zone Plate 26. The concentric circles 27 are drawn so thatthe difference in path length between adjacent transparent zones to apoint on the axis 28 of the zone plate is just equal to λ, thewavelength of the incident radiation. FIG. 9(b) shows the parameters forthe following formulae. Referring to FIG. 11(b), for this pathdifference to occur: $\begin{matrix}{r_{n}^{2} = {{n\quad F\quad \lambda} + \frac{n^{2}\lambda^{2}}{4}}} & \lbrack 11\rbrack\end{matrix}$

where:

r_(n)=radius of the nth zone

n=number of zones subtended by r_(n)

F=primary focal length

λ=wavelength of the incident radiation

If n is small, the radii are given approximately by:

r _(n) ² =nFλ  [12]

If a plane wave is incident on the zone plate, the diffracted wavespassing through the transparent zones and arriving at the point F on thezone plate axis will interfere constructively with each other. The pathdifferences for all the transparent zones are an integral number ofwavelengths. An image of the source emitting the plane waves will beformed at the point F on the axis of the zone plate.

From equation 12, $\begin{matrix}{F = \frac{r_{n}^{2}}{n\quad \lambda}} & \lbrack 13\rbrack\end{matrix}$

Also a point at a distance s in front of a Fresnel Zone Plate will beimaged at a point s′ behind the zone plate as given by: $\begin{matrix}{{\frac{1}{s} + \frac{1}{s^{\prime}}} = \frac{1}{F}} & \lbrack 14\rbrack\end{matrix}$

This is the same expression as that used for a thin lens. Using theRayleigh Criterion for the formation of optical images, it can also beproven that angular resolution of a zone plate is the same as for a lensof the same aperture and is given by:

 sin θ=1.22(λ/D)  [15]

Equation 13 shows that the focal length of the zone plate is inverselyproportional to the wavelength of the incident radiation. In the visiblespectrum, there is approximately a 2:1 variation in λ; therefore, therewill be a 2:1 variation in the focal length of a zone plate over thisregion and 1,000:1 variation in focal length in the region extendingfrom the near infrared (10⁴ Å) down to the soft X-Ray (10 Å)wavelengths. Therefore, the zone plate is inherently a highlymonochromatic device.

If a plane wave is incident on a Fresnel Zone Plate, several diffractedwaves are generated. These are separated into three categories:positive, negative and zero orders. The positive orders consist of anumber of wavefronts converging toward the axis of the FZP; the negativeorders are those wavefronts which appear to diverge from points alongthe axis in front of the zone plate; and the zero order consists of aplane wave similar to the incident wave, but reduced in amplitude. FIG.11 illustrates the basic theory of the zone plate. As can be seen inFIG. 11, a plane wave will not only focus at the primary focal point F(65), but also with successively lower intensity, at a distance from thezone plate of F/3, F/5, F/7, etc. The diverging wavefronts appear toemanate from points along the axis in front of the zone plate at −F,−F/3, −F/5, etc. The zero and negative order wavefronts may be removedfrom the point at which the positive order wavefronts focus by placing astop so that it blocks off the inner zones of the zone plate, or bysimply not forming the inner zone of the zone plate.

A Gabor Zone Plate is defined as that zone plate which, when illuminatedby spherical (or plane) wavefronts of monochromatic light, produces onlyone real and one virtual point image. A schematic of this is shown inFIG. 12. The zero-order represents that light passing through the zoneplate that is not used to produce an image. The +1-order represents thatlight used to focus the real image, and the −1-order represents thatlight used to focus the virtual image. This zone plate can be producedphotographically or by holography on an emulsion whose developing powervaries sinusoidally as the intensity of the incident light, or it can bestamped onto plastic. FIG. 13 shows a schematic of a Gabor Zone Platethat has been produced holographically. Note the absence of physicalfeatures on the surface of the emulsion. (This is not quite true, sincea developed emulsion would have some physical features. It is true thatsome “surface holograms” perform active focusing by using surfacefeatures of the developed emulsion. However, holograms often performactive focusing by using diffractive properties caused by differentfeatures within the volume of the emulsion. These are called “volumeholograms” or “Bragg Angle Holograms.”)

Refer to equation 11. Since the focus is different for each wavelenth,for the magnification principle to hold true for zone plates illuminatedwith white light, the following equation must be true:${{\left( \frac{F_{2}}{F_{1}} \right)\lambda_{1}} = {\left( \frac{F_{2}}{F_{1}} \right)\lambda_{2}}},$

in other words, the ratio of focal lengths both before and aftermagnification must be the same for all wavelengths. We now obtain:$\frac{\left( {F_{2}/F_{1}} \right)\lambda_{2}}{\left( {F_{2}/F_{1}} \right)\lambda_{1}} = {\frac{\left( \lambda_{2}^{2} \right)}{\left( \lambda_{1}^{2} \right)}\frac{\left\lbrack {{4\left( r_{n}^{2} \right)_{1}\left( {\beta - 1} \right)} + {n^{2}{\lambda_{1}^{2}\left( {3 - \beta} \right)}}} \right\rbrack}{\left\lbrack {{4\left( r_{n}^{2} \right)_{1}\left( {\beta - 1} \right)} + {n^{2}{\lambda_{2}^{2}\left( {3 - \beta} \right)}}} \right\rbrack}}$

where:

n=number of fringes

β=magnification

This can be approximated by: $\begin{matrix}{\frac{\left( {F_{2}/F_{1}} \right)\lambda_{2}}{\left( {F_{2}/F_{1}} \right)\lambda_{1}} = \left( \frac{\lambda_{2}^{2}}{\lambda_{1}^{2}} \right)^{2}} & \lbrack 16\rbrack\end{matrix}$

Therefore, when dealing with zone plates, the basic magnificationprinciple, upon which this application is based, does not hold true forwhite light. It could work if the lenslets were to be arranged so thatthe focal lengths for the different primary wavelengths alternate; theneach lenslet would require an attached color filter, and a color filterwould then become part of the matrix lens array as is shown in FIG. 14.

FIG. 14 is a schematic of a zone plate matrix lens array optical systemFIG. 14(a) represents a cross section of the matrix lens array opticalsystem, while FIG. 14(b) shows a schematic of how this optical systemworks. The optical system consists of both a matrix zone plate array 29and a color plate 30. Both these elements in combination serve toproduce a two-dimensional image of two-dimensional elemental photographson a focal plane or film plane 31. The elemental photographs alternateas monochromatic blue, red and green pictures. It is less desirable touse color film than black-and-white film due to the higher resolution ofblack-and-white film. Playback with another color plate will reproducethe blue, red and green monochrome colors associated with each elementalphotograph, and, if the elemental photographs are unresolvable by theaudience due to minimum visual acuity, a viewer will see a reconstructedimage in full color.

FIG. 15 is a schematic of a zone plate matrix lens array optical systemwith vertical parallax eliminated. This consists of a series ofcylindrical zone plates arranged horizontally 32 and a color plate 33.Of course, the optical system must also contain a means 34 for focusingin the vertical direction. Such focusing means can consist of a singlecylindrical zone plate 35 or a cylindrical lens 36.

Use of the alternate lens embodiments could present film resolutionproblems. However, in the photographic industry, film manufacture isconstantly being improved, and higher film resolution is becomingavailable. Once sufficient film resolution has been achieved, many ofthe resolution economies discussed for the preferred embodiment will notbe necessary. Therefore, the alternate lens design embodiments maybecome desirable at that time.

However, the resolution problems could be due to conditions other thanfilm resolution limitations (viz., diffraction and abberations). Whenexamining the resolution limitation due to film resolution, it must beunderstood that the resolvable distance, d, upon the film is given by$\begin{matrix}{{{d = \frac{1}{R}},{mm}}\quad} & \lbrack 17\rbrack\end{matrix}$

With a film resolution of 400 lines/mm, the smallest resolvable spotwould be 0.0025 mm.

We now examine the resolution limitation due to diffraction. Considerthe fact that each lenslet is a pair of crossed cylinders, each having ahorizontal dimension of φ and a vertical dimension of δ. For diffractioncalculations these lenslets can be represented by a rectangular aperturewhose dimensions are φ×δ. The Franhoffer Diffraction from this aperturegives an expression for the intensity at any point P: $\begin{matrix}{{I(P)} = {{\left( \left\lbrack \frac{\sin \quad \left( {{kp}\quad {\varphi/2}} \right)}{{kp}\quad {\varphi/2}} \right\rbrack \right)^{2}\left\lbrack \frac{\sin \quad \left( {{kq}\quad {\delta/2}} \right)}{{kq}\quad {\delta/2}} \right\rbrack}^{2}I_{o}}} & \lbrack 18\rbrack\end{matrix}$

where I_(o) is the intensity at the center of the pattern, and is givenby: $\begin{matrix}{I_{o} = \frac{EA}{\lambda^{2}}} & \lbrack 19\rbrack\end{matrix}$

where E is the total energy incident upon the aperture and A is the areaof the aperture.

A=φδ

Equation [18] shows that the intensity is the product of two similarexpressions, one depending on the horizontal dimension and the other onthe vertical dimension of the rectangular aperture. The expression:$y = \left( \frac{\sin \quad x}{x} \right)^{2}$

has the following maxima and minima:

x y 0.000    1.00000 1.000 π 0.00000 1.430 π 0.04718 2.000 π 0.000002.459 π 0.01694 3.000 π 0.00000 3.470 π 0.00834 4.000 π 0.00000 4.479 π0.00503

When comparing this with the Franhoffer Diffraction Pattern for acircular aperture, we look at the expression:$y = \left( \frac{2{J_{1}\lbrack x\rbrack}}{x} \right)^{2}$

This expression has the following maxima and minima:

TABLE 3.2 CIRCULAR APERTURE x y 0.000    1.0000 1.220 π 0.0000 1.635 π0.0175 2.233 π 0.0000 2.679 π 0.0042 2.238 π 0.0000 3.699 π 0.0016

The abscissa of the first lobe of the diffraction pattern for therectangular aperture in the horizontal direction: $\begin{matrix}{{p = {\pm \frac{\lambda}{\varphi}}}{{{because}\quad {kp}\quad {\varphi/2}} = {{{\pm u}\quad \pi \quad \left( {{u = 1},2,3,\ldots}\quad \right)\quad {and}\quad k} = {\frac{2\quad \pi}{\lambda}.}}}} & \lbrack 20\rbrack \\{{{Also}\text{:}\quad q} = {\pm \frac{\lambda}{\delta}}} & \lbrack 21\rbrack\end{matrix}$

because kqδ/2=±νπ(ν=1,2,3, . . . )

Comparing this with the abscissa of the Airy Disc for a circularaperture: $r = {\pm \frac{1.22\quad \lambda}{D}}$

where D is the diameter of the aperture.

The basic difference between the diffraction pattern of a rectangularaperture and a circular aperture is that much less of the energy is inthe central lobe for a rectangular aperture than for a circular one. Ina rectangular aperture, the secondary maxima are of greater importance.However, most of the energy does go into the central lobe, and it can beconsidered to be the prime characteristic of the diffraction pattern.Actually, p and q are angles, and the actual diameter of the minimumspot which can be produced at the focal plane by a lens is

d=2ƒθ  [22]

Substituting equations [20] and [21] into equation [22], we obtain:$\underset{horizontal}{a} = {{{{2{\lambda \left( {F/\#} \right)}_{1}}\quad\&}\quad \underset{vertical}{b}} = {2{\lambda \left( {F/\#} \right)}_{2}}}$

where a & b are the dimensions of the rectangular central lobe, (F/#)₁is the numerical aperture of the lens in the horizontal direction, and(F/#)₂ is the numerical aperture of the lens in the vertical direction.

Consider an example where (F/#)₁=1.7 and (F/#)₂=1.2, and use thewavelength,

λ=5,000 Å. Then,

a=0.0017 mm

b=0.0012 mm.

Therefore, the smallest spot that can be focused by the above lenslet isa rectangle whose horizontal dimension if 0.0017 mm and whose verticaldimension is 0.0012 mm. This means that the resolution limitation due todiffraction for this lenslet would be 585 lines/mm in the horizontaldirection and 825 lines/mm in the vertical direction.

We now examine the resolution limitation due to abberation. FIG. 16shows abberation in a cylindrical lens. As can be seen, point A from theobject transmits directly along an axis perpendicular to the axis of thecylindrical lens and appears as image point A′. However, it can be seenthat image point A′ can appear as a multiplicity of points on the imageplane. Refer to FIG. 17. FIG. 17(a) is an optical ray trace showingabberation in a cylindrical-spherical lenslet. FIG. 17(b) is a graphshowing the spread of focus due to abberation. From FIG. 17(a) theradius of curvature of the lens is r and the relative aperture is ω towhich is defined by the equation: $\begin{matrix}{{\tan \quad \omega} = \frac{4\left( {F/\#} \right)}{{4\left( {F/\#} \right)^{2}} - 1}} & \lbrack 23\rbrack\end{matrix}$

which will be derived later. Therefore, $\begin{matrix}{\left( {F/\#} \right) = \frac{1}{2\quad {\tan \left( {\omega/2} \right)}}} & \lbrack 24\rbrack\end{matrix}$

Now, according to equation [23], when the (F/#) is 1.7, ω is 32.8°. Theradius of the lens is given by:

r=ƒ(η−1)  [25]

When η=1.53, φ=1.0 mm and ƒ=1.7 mm, r=0.90 mm. From FIG. 16(b):W_(A)/2r=6.8×10⁻³. W_(A)=0.01224 mm and the resolution is 81.7 lines/mm.

The problem of lens abberation from a 1 or two meter long cylindricallens can be solved by using a cylindrical Fresnel Zone as shown in FIGS.15 and 18. In these cases the cylindrical zone plate 35 is situated sothat the focusing occurs in the horizontal direction only. In FIG. 15, acylindrical zone plate array 32 (in combination with a color plate array33) is used to provide focusing in the vertical direction so that thecombination of lens systems 35 with 32 produces the two-dimensionalarray of elemental pictures. In FIG. 18, the cylindrical zone plate 35is also situated so that the focusing occurs in the horizontal directiononly. However in this case, a Bonnet Screen 37 consisting of verticalcylindrical lenslets is used to provide focusing in the verticaldirection so that the combination of lens systems 35 and 37 produces thetwo-dimensional array of elemental pictures 38. In the case of FIG. 18,a color plate array is not required.

When selecting the resolution parameters of camera systems, one mustselect these parameters according to the minimum resolution figures. Forexample, cylindrical lenses are available of 1 mm diameter having aresolution of 400 lines/mm. It would be useless, therefore, to use afilm whose resolution is 2,000 lines/mm. No element in the opticalsystem need possess a greater resolution than that optical elementnecessarily possessing the worst resolution.

Much of the resolution problems resulting from the alternate embodimentscan be avoided by implementing yet another alternate embodiment i.e., amultistage camera. This is shown schematically in FIG. 19. In this case,several camera stages of the type shown in FIG. 5 are positionedhorizontally within the same camera housing so as to be exposed onseveral film frames. Clearly the lenses, matrix lens arrays, colorplates, and multiplexing optics need not be the same number as thenumber of film frames. The key issue is that multiple film framesarranged horizontally are used. One can even design a single camerastage that will focus different sections of the two-dimensionalelemental array on multiple film frames. In this way, because each filmframe contains only a fraction of the information contained within thepreferred embodiment, the resolution requirements are decreased by afactor of the number of frames used.

Another aspect of an alternate embodiment in the camera design would bethe use of holographic optics to accomplish the dissection andmultiplexing performed by the fiber optics image dissector andmultiplexer in the preferred embodiment. This is shown conceptually inFIG. 20. In this case, reflection holograms would be used because oftheir high diffraction efficiency (95-100%), although the process wouldwork conceptually even with transmission holograms. (The diagrams,however, are shown using reflection holograms.) This process involvesthe transfer of images from one holographic plane to another plane with1:1 magnification. (Several methods exist to provide abberation freemagnification using holography, should this be desirable.) In thefigure, the image 39 is projected through the camera matrix lens array40 or otherwise focused onto hologram plane 41 which, in turn, projectsthe appropriate multiplexed frame onto the film, 42, using intermediateholographic planes (shown symbolically as planes 43) if necessary. Theseintermediate planes serve the purpose of allowing the image to impingeonto the film from a far less severe angle, thereby decreasing theabberations. But, these intermediate planes may not be necessary. FIG.21 shows conceptually how such a holographic plane can be made. Forclarity, multiplexing will be accomplished, in this figure, for only tworows. The image on the left with two rows, 44 and 45, arrangedhorizontally is projected using lens 46 onto hologram 47. This projectedimage acts as a reference beam for the hologram, therefore,reconstructing an object beam which focuses an image in space 48,consisting of rows 44 and 45 arranged vertically.

The final design consideration for the camera occurs where its use toproduce three-dimensional motion pictures is desired. The usualproduction of motion pictures depends upon a viewer's persistence ofvision to interpolate still images from multiple frames. In aconventional motion picture, a certain amount of flutter (ormisregistration of the picture on the screen) from frame to frame can beallowed before the audience begins to be bothered by it. Obviously, anymovement less than minimum visual acuity would not be noticed. Thisresolution is one-minute of arc or approximately 3×10⁻⁴ radians.Assuming a minimum seating distance of twice the screen width, apractical maximum level of misregistration would be:

(6W×10⁻⁴) or (±3W×10⁻⁴)

where W is the screen width. Considering a ten-meter wide screen,permissible maximum flutter would be ±3 mm or a total flutter of 6 mm.Actually, misregistration is greater than this figure andmisregistration which exceeds the acceptable limits manifests itself inimage defocus. This defocus is often tolerated and frequently goesundetected by much of the audience. Of course, as the flutter becomesgreater, the entire picture begins to jitter.

For integral photography, as the projected image moves with respect tothe screen, the three-dimensional image will move also (as a unit).Therefore, flutter would result in a blurring of the three-dimensionalimage. However, the problem is far more severe for integral photographythan for conventional photography. Were the projected image within eachelement to be misregistered with respect to the central position of eachelemental lens on the screen by a given percentage, the reconstructedthree-dimensional image will move with respect to the screen boundariesby the same given percentage. Since the field in which the image canmove horizontally is confined to a certain percentage of each element,and since there are 1,730 elements in the horizontal field, the maximumallowable misregistration in the horizontal direction is a factor of1/1,730 times that of conventional films, or:

 Δw=±1.375×10⁻⁷  [26]

where w=the width of the film frame. The same misregistration is allowedfor the vertical direction. (It will be seen later that misregistrationin the vertical direction will not be important. Furthermore, anyvertical misregistration can be dealt with in the same manner ashorizontal misregistration.) It is important to note at this point thatif conventional film frame format is used with commercially availablefilms, the registration tolerance becomes prohibitive.

Misregistration of the picture on the screen may be caused by severalfactors:

(1) side-to-side motion of the screen, which may be compensated for;

(2) misregistration of the film, which, based upon calculations, shouldbe held to one-half micron for best results; and

(3) projector motion, mainly due to vibration, which may be divided intotwo components:

(a) Translation:

[1] Forward Lateral—This type of motion affects the focus.

[2] Vertical—Registration is not critical here if vertical parallax iseliminated.

[3] Sideways Lateral—This is the most critical of translatory movements.Whatever the absolute motion of the projector, this will be the screenmisregistration. For a ten-meter wide screen, the comfortable upperlimit of movement is about 2.85 microns.

(b) Rotation (Refer to FIG. 22):

[1] X-Axis Rotation—This can cause some misregistration but is nothighly critical.

[2] Y-Axis Rotation—This is not critical as it will cause only verticalmisregistration.

[3] Z-Axis Rotation—This is critical and must be held to below about0.0347 arc-seconds.

The problems discussed in this section concerning jitter are important,as they must be taken into consideration in the designs of both thetheater and the screen. However, the solution to these problems must beattended to in the designs of both the camera and the projector.

Refer to FIG. 23(a). Assume an object point P₁ which appears on thescreen 49 as a multiplicity of points P₁′. Should the points P₁′ bemisregistered to P₂′, a distance of Δx′, the image point P₂ will bemisregistered with respect to P₁ by a distance Δx, such that:$\frac{\Delta \quad x}{\Delta \quad x^{\prime}} = \beta$

Where β is the magnification factor of each lenslet. This argument holdstrue whether the image is real or virtual. Referring to FIG. 23(b):

β=s/s′

but s′≈ƒ. Therefore,

β≈s/ƒ

where ƒ is the focal length of each lenslet, and s is the distance fromthe screen to the image (assuming a virtual image).${\Delta \quad x^{\prime}} = {\frac{\Delta \quad x}{\beta} = \frac{\Delta \quad {xf}}{s}}$

The viewer will observe the image shifting by:

$\begin{matrix}{\underset{\text{MAXIMUM~~~TOLERABLE}}{\Delta \quad x} = {\alpha \left( {V + s} \right)}} & \lbrack 27\rbrack\end{matrix}$

where v is the viewing distance from the screen and α is the angle ofminimum visual acuity. Therefore,${\Delta \quad x^{\prime}} = {{\frac{\alpha \quad {f\left( {V + s} \right)}}{s}\quad {or}\quad \Delta \quad x^{\prime}} = {\alpha \quad {f\left( {\frac{V}{s} + 1} \right)}}}$

Since α=2.91×10⁻⁴ and V=2W (where W is the width of the screen, then$\begin{matrix}{{\Delta \quad x^{\prime}} = {2.91 \times 10^{- 4}{f\left( {\frac{2W}{s} + 1} \right)}}} & \lbrack 28\rbrack\end{matrix}$

As the reconstructed image moves further away from the viewer, themaximum screen misregistration (so as to maintain acceptable quality)becomes smaller and smaller. The worst case is when the image is atinfinity. Therefore, since some objects will be at infinity, we cantolerate a maximum misregistration of

Δx′=2.91×10⁻⁴ƒ  [29]

To express this equation in more convenient terms,

ƒ=D(F/#), and D=W/n Therefore, $\begin{matrix}{{\Delta \quad x^{\prime}} = {2.91 \times 10^{- 4}\frac{W}{n}\left( {F/\#} \right)}} & \lbrack 30\rbrack\end{matrix}$

Let us now cite an example. In this case, W=10 meters, n=1,730, and(F/#)=1.7. Therefore, Δx′=2.85 μ. For a ten-meter screen and for imagesat infinity, to estimate the amount of misregistration tolerable forimages not at infinity, from equation [28]. $\begin{matrix}{{\Delta \quad x^{\prime}} = {2.91 \times 10^{- 4}{f\left( {\frac{2W}{s} + 1} \right)}}} & \lbrack 31\rbrack\end{matrix}$

Using our example:

${\Delta \quad x^{\prime}} = {\frac{5.70 \times 10^{- 4}}{s} + 2.85}$

Distance of Image from Screen Maximum Tolerable Misregistration s, μ x′,μ 0 ∞ 1 m = 10⁶ 59.85 2 m = 2 × 10⁶ 31.35 10 m = 10⁷ 8.55 100 m = 10⁸3.14 ∞ 2.85 Δx′ is the maximum allowable misregistration for an imagelocated at a distance s from the screen to be in best focus.

Now, maximum tolerable misregistration of the film is less than themisregistration allowed for the screen, since magnification takes placeduring projection. Therefore, the expressions for Δx_(F) become:${\Delta \quad x_{F}} = \frac{\Delta \quad x^{\prime}}{M}$

where:

Δx_(F) is the maximum allowable film misregistration,

Δx′ is the maximum allowable screen misregistration, and

M is the magnification factor for projection.$M = \frac{\varphi_{S}}{\varphi_{C}}$

where:

φ_(S) is the width of a cylindrical lenslet in the screen, and

φ_(C) is the width of a cylindrical lenslet in the lens array of thecamera.

Substituting these two equations into the equations above, respectively,and remembering that φ_(C) (F/#)=ƒ_(C), we obtain $\begin{matrix}{{\Delta \quad x_{F}} = {2.91 \times 10^{- 4}{f_{C}\left( {\frac{2W}{s} + 1} \right)}}} & \lbrack 32\rbrack\end{matrix}$

$\begin{matrix}{{\lim\limits_{S\rightarrow\infty}{\Delta \quad x_{F}}} = {2.91 \times 10^{- 4}f_{C}}} & \lbrack 33\rbrack\end{matrix}$

In our example, M=5.78

s, μ Δx_(F), μ 0 ∞ 10⁶ 10.18 2 × 10⁶ 5.42 10⁷ 1.480 10⁸ 0.543 ∞ 0.493

Therefore, the maximum tolerable film misregistration with respect tothe camera and projector (so that objects at infinity will be in focus)is ½-micron on the film.

Since it is required to register each frame within ½-micron in thesideways lateral direction, we must employ a 3-point registrationsystem. The semiconductor industry currently registers photographicmasters to within one-micron using this method, and for holographicinterferometry, registration of 0.3-micron is common. Obviously,standard sprocket holes cannot adequately register the film. However,three reasonably sized heavy duty holes can. Referring to FIG. 24(a), wesee the positioning of the registration holes 50 on the frame. Ofcourse, these holes may be located anywhere on the frame. The regularsprocket holes 51 can be used to move the film through the camera andthe projector, but the film must be stopped for each frame and threeprobes move out to enter the three registration holes 50 and to registerthe film. It is obvious that the three registration holes 50 must beboth accurately positioned and sized. FIG. 24(b) shows how these holescan be manufactured. Three accurately positioned wedge shaped circularconventional punches produce holes in each frame. With the punch and dyeset 52 shown in the figure, the diameter of the holes can be easilycontrolled. FIG. 24(c) illustrates one method of registering the film inthe camera or projector using the registration holes. When the film isstopped for the exhibition of the frame, three registration cones 53enter the holes as is shown in the figure, and mate with registrationcaps 54 on the other side of the film. The registration cones arespring-loaded such that when contact with the film is made, noadditional pressure is applied. The cones position each frame both inthe plane of the registration caps and with respect to the centralposition of the registration caps. Stripper plates 55 then come from thesides and make contact with both the film and the cones 53. These platesapply pressure to the film to position it firmly in the plane of theregistration caps 54. In this manner, each frame is kept in perfectregistration both in the sideways lateral position and with respect tothe focal plane of the lens. It is important that the cones emerge andretract while the film is stopped. If the film is looped properly, thefilm in the gate can be kept free of tension or compression. The film isthen both stopped and positioned by the emerging cones. This can beaccurately performed at the required film speeds.

There are two additional problems which must be dealt with in order toregister the photograph with respect to each frame. It is one thing toregister the film itself, but unless the photographic information ispositioned accurately on the film, gross movement of the projected imagewill occur. Since registration must be held to within ½-micron, the twoconsiderations are that dimensional changes in the film must be avoided,and emulsion shrinkage must be eliminated. The former problem can besolved by using thicker film, and the latter problem can be solved byprocessing the film properly. The latter problem will be discussed laterin the section on intermediate processing, but it should be noted herethat such processing has been used for holographic interferometry wheredimensional changes of as much of half the wavelength of the light used(this is usually 0.3-0.4 μ) will invalidate the measurement.

Once a film has been produced by the cameras described above consistingof single photographs or frames wherein the two-dimensional array ofelemental photographs has been recorded thereon, such photographs orframes must be projected in such a manner that a magnifiedthree-dimensional image of the original scene would be visible to anaudience. For the process and system described herein, a special screenand projector are required. In order to continue with a discussion ofthe screen and projector design, certain theater design considerationsmust be taken into account. When producing three-dimensional pictures ina theater by wavefront reconstruction, audience placement is dictated bythe type of image that is projected. The different types of projectedthree-dimensional images are illustrated in FIG. 25. An audience 56 willgenerally see a projected three-dimensional virtual image 57 asappearing behind the screen 58 while it will generally see a projectedthree-dimensional real image 59 appearing in front of the screen 58.

For real image projection, severe limitations exist on theater design.When virtual images are projected to appear behind screen, it is notessential that the complete image be visible. In that case, if theperiphery of the scene is blocked by the screen boundaries, it is notimportant, especially if the action takes place in the center of thescreen. For a real image, the above is not the case. Since a real imageis projected in front of the screen, a partially visible image may seemweird because those parts of the image which the audience cannot seewill just be invisible. It does not have the excuse that the screenboundaries block those parts of the object which are not visible. Thoseparts of the object which are not visible will just seem to disappear.Furthermore, spectators seated in different parts of the theater willobserve different parts of the object. The theater should be designedfor real image projection to achieve optimum viewing conditions so thatthe entire object will be completely visible to every member of theaudience. This can place a severe limitation on where the audience maybe placed.

FIG. 26(a) illustrates the case where a real image larger than thescreen is projected into the theater. An arrow AB has been used as theobject. In order for a member of the audience (not shown) to see theentire arrow, both points A and B must be visible simultaneously. Thatis only possible if light from both points A and B reach his eyes. FIG.26(a) is, therefore, an optical ray trace to determine the size of theaudience. Point A is only visible in the triangular area 60 on the left,while point B is only visible in the triangular area 61 on the right. Inthe central region 62, neither points A nor B are visible, meaning thatthe central portion of the arrow can be seen but not the outerboundaries. For best results, a theater should not be designed for realimage projection when the size of the projected image is larger than thescreen.

FIG. 26(b) illustrates the case where a real image smaller than thescreen is projected into the theater. Once again, a ray trace is used todetermine the size of the audience in which all spectators will see bothpoints A and B. Point B is not visible within the tetragonal area 63 onthe left, while point A is not visible within the tetragonal area 64 onthe right. Only in the central triangular area 65 can both points A andB, and, therefore the entire object, be seen. The seating of theaudience 66, for best results, should be arranged within triangular area65 as illustrated in the figure.

For comparison purposes, FIG. 26(c) illustrates some of the concepts oftheater design for virtual image projection. In this case, consider CDto be the same size as the entire scene, and arrow AB to be the size ofthe region in which the action takes place. Outside of the centraltriangular region 67, the entire scene CD will not be completelyvisible. However, except for the two triangular regions 68 and 69 onboth left and right, the center of action AB can be seen throughout therest of the theater. The audience can be seated so that all or most ofAB will be seen. This concept is similar to a live theater presentationwhere no two members of the audience see the scene identically, and somemembers of the audience have their view partially obstructed.

When looking at FIG. 26(c), from a very simple viewpoint, it becomesobvious that, for the same size theater, a virtual image process willlikely be more economical than a real image process, as it canaccommodate more spectators. This would be so if the only thing to worryabout was the production of three-dimensional images by wavefrontreconstruction. However, integral photography imposes one additionalsevere limitation on theater design than does holography, i.e., thetotal angle under which a spectator sitting on the perpendicularbisector of the screen views the three-dimensional virtual image cannotbe greater than the acceptance angle, ω, of each individual lenslet inthe matrix lens array. The parameters for the determination of thisacceptance angle are shown in FIG. 8. $\begin{matrix}{{\tan \quad \frac{\omega}{2}} = {\frac{\varphi_{C}}{2f_{C}} = \frac{1}{2\left( {F/\#} \right)}}} & \lbrack 34\rbrack\end{matrix}$

However:${\tan \quad \omega} = \frac{2\quad {\tan \left( \frac{\omega}{2} \right)}}{1 - {\tan^{2}\left( \frac{\omega}{2} \right)}}$

Therefore: $\begin{matrix}{{\tan \quad \omega} = {\frac{4\quad \varphi_{C}f_{C}}{{4f_{C}^{2}} - \varphi_{C}^{2}} = \frac{4\left( {F/\#} \right)}{{4\left( {F/\#} \right)^{2}} - 1}}} & \lbrack 35\rbrack\end{matrix}$

The above equation shows that the acceptance angle, ω, is dependent onlyon the (F/#) of each lenslet. FIG. 27 shows the acceptance anglelimitation. From FIG. 8 we can see that each lenslet in the lens arrayhas the same acceptance angle. This angle limits the ratio of objectsize to distance from the camera or screen. It is obvious that the totalacceptance angle of the lens array of the camera or screen will also beω. A spectator in the audience seated within the triangular area 70shown in FIG. 27 can see more of the scene than is allowed by theacceptance angle limitation. This, however, is not possible. Onlyoutside this triangle can a viewer see less than the total sceneencompassed by the angle ω. Anyone sitting inside the triangle will seea very confusing picture which is caused by a phenomenon denoted here bythe term “flipping”. Wherever in the theater the total viewing angle isgreater than ω, the scene will begin to repeat itself. The image atthese points will appear double. This phenomenon of scene repetition asthe viewing angle changes is called flipping. Flipping will occur over atotal angle of ω/2. This places a practical limitation on where theaudience may sit. No viewers should be placed in the area in which adouble image can be seen. FIG. 28 shows the areas in which a doubleimage can be seen, and in which the audience can be seated. In thisfigure, the theater is divided into five pairs of acceptable areaswithin which the audience can be seated. In each of these areas, theaudience will see the entire picture, since the flipping phenomenoncauses the scene to be repeated each time flipping occurs. Each of thefive areas 71, 72, 73, 74, 75 consists of three regions: the first isthe tetragonal area closest to the screen, then followed by a triangulararea and then by an area bounded by two parallel lines at a distanceaway equal to the width of the screen and going to the rear of thetheater with no limit. FIG. 29 shows the appropriate geometricparameters used for calculation.

From ΔXYZ: $\begin{matrix}{{\frac{2c}{W} = {\cot \quad \omega}}{c = {\frac{W}{2}\cot \quad \omega}}} & \lbrack 36\rbrack\end{matrix}$

where:

W=the width of the screen

c=the distance to the first tetragonal area.

From ΔUXY: $\begin{matrix}{{b + c} = {\frac{W}{2}\cot \quad \left( \frac{\omega}{2} \right)}} & \lbrack 37\rbrack\end{matrix}$

and, finally, ΔSTU≅ΔUXY. Therefore,

a=b+c, and

$\begin{matrix}{{{a = {b + c}},\quad {and}}{{a + b + c} = {W\quad {\cot \left( \frac{\omega}{2} \right)}}}} & \lbrack 38\rbrack\end{matrix}$

where:

b+c=distance from the screen to the triangular area, and

a+b+c=distance from the screen to the rectangular area.

Substituting equation [34] into equation [36] $\begin{matrix}{c = {\frac{W}{2}\left\lbrack \frac{{4\left( {F/\#} \right)^{2}} - 1}{4\left( {F/\#} \right.} \right\rbrack}} & \lbrack 39\rbrack\end{matrix}$

Substituting equation [35] into equation [37]

b+c=W(F/#)  [40]

and, finally, from equation [38]

a+b+c=2W(F/#)  [41]

Returning for the moment to the theory of real image projection, we mustnow examine its compatibility with virtual image projection. As can beseen from FIG. 28, the triangular area for virtual image projection inarea 71 is identical to the acceptable area for real image projectionshown in FIG. 11(b). Since the real image acceptable area overlaps eventhe rectangular region of area 71, the entire area 71 is suitable forviewing projected real images, provided that the size of the image isnot so large as not to enable it to fall within the triangular region ofcomplete visibility just in front of the tetragonal region shown in FIG.28 or in FIG. 26(c). Similarly, as each area (71, 72, 73, 74 and 75)sees its own complete scene, it also has its own projected real images.Therefore, the same rule for acceptability of such real image projectionapplies in each of the five areas. Of course, the real image cannot beseen in the tetragonal region, even though the virtual image can be seenin this region.

Now, it must be understood that a screen used with this process for thecreation of three-dimensional images before a theater audience must bean active optical element of the entire optical system used forprojection. The screen itself must contain a matrix lens array havingthe same number of elements (or lenslets) and in the same configurationas the camera matrix lens array used to photograph the scene. Thisprinciple is illustrated in FIG. 1 as the basic method of magnificationand projection.

The preferred embodiment of the screen is an array of cylindrical zoneplates with associated color filtration. Zone plates can be producedholographically. However, instead of being produced as transmissionholograms, they are produced as reflection holograms. Reflectionholograms are commonly manufactured by a process called Bragg-AngleHolography. In this instance, instead of the diffraction pattern beingformed on the surface of the photographic emulsion which makes up thehologram, the diffraction pattern is formed in the volume of theemulsion itself. Such a holographic zone plate would have the followingadvantages:

(1) Since it is formed as a reflection hologram, this type of screen isapplicable to front projection, the technique now in use in mosttheaters.

(2) A reflection holographic screen accepts white light emanating from apoint source and reflects it into the audience at the wavelength withwhich the hologram was initially made. Since the zone plate screenconsists of a mosaic of alternating zone plates, each one produced as ahologram by laser light having a different wavelength, it becomesobvious that a holographic screen of this type already has its own colorplate “built-in”. Separate color filters are not required.

The screen is a Bragg Angle Reflection Hologram, which when illuminatedfrom the front with a beam of white light having a spherical wavefront,the reconstruction will be a series of thin vertical lines, each line adifferent color, the colors alternating between red, green and blue,each line projected in front of the screen a distance ƒ, and thevertical lines will be arranged horizontally across the width of thescreen. A Bragg Angle Hologram is really a diffraction grating whosediffracting elements are distributed throughout the volume of theemulsion. A reconstruction can only be obtained by a reference beam ofthe same wavelength as was used to make the hologram. For thiswavelength, the reconstruction efficiency is extremely high. If a whitelight reference beam should be used, only the appropriate colorcomponent will be selected to perform the reconstruction.

FIG. 30(a) shows the fabrication of a reflection hologram withmonochromatic light. The reference beam is a spherical wavefront and thereconstruction is a real image of a single vertical line projected infront of the hologram. The object beam is created by passing a laserbeam 76 through a cylindrical lens 77 which focuses through a slit 78positioned at a distance ƒ from the photographic plate 79. Thisoperation can be performed separately for each wavelength needed, or thehologram can be fabricated as shown in FIG. 30(b). A white light, ormulti-wavelength laser 80, such as a krypton laser, is used. Thecomplete beam having all color components is used as the reference beam84. The laser beam is split in two using a beam splitter 81 into twocomponents 82 and 83. Beam 82 ultimately becomes the reference beam 84after passing the optical components (mirrors M₁, M₂ and M₃, and concavelens L₁ and circular aperture S₁). Beam 83 ultimately becomes the objectbeams. First, the color components are separated by a prism 85. Theunwanted wavelength components are removed by mirrors M₀ and M₃ leavingonly the three red 86, green 87 and blue 88 object beams to be used tocreate the hologram. (Of course, colors other than red, green and bluecan be used as long as they are complementary colors which are used toform white.) Thus far only three zone plates have been created on thephotographic plate 89. The photographic plate 89 is then moved, and anew section is exposed in exactly the same manner. The method ofreconstruction is shown in FIG. 31. A white light reference beam with aspherical wavefront is used to reconstruct alternating red, green andblue cylindrical wavefronts. Should the reference beam emanate from aprojector in the rear of the theater with the image of an integralphotograph impressed on the beam such that the image of the integralphotograph is focused onto the screen, then a three-dimensional imagewill be reconstructed from the integral photograph. In this case, acolor filter is not required, as the image will be properly broken downinto the appropriate color pattern, and black & white film must be used.

Alternate embodiments for the screen are as follows. In one alternateembodiment, the screen can be comprised of spherical lenslets that arehexagonally close-packed. This concept is shown in FIG. 32. The screen90 consists of spherical lenslets 91, each lenslet being surrounded bysix other spherical lenslets. This type of screen would be used if thecamera optics used are those previously described as an alternate cameraembodiment and depicted in FIG. 9.

In another alternate embodiment, the screen can be comprised of crossedcylindrical lenslets (i.e., a fly's eye lens). This concept is shown inFIG. 33. FIG. 33(a) is a top view of the device while FIGS. 33(b) and33( c) represent side and front views respectively. This device 92consists of two crossed cylindrical matrix lens arrays or BonnetScreens. Each of these two matrix lens arrays or Bonnet Screens arecomprised of cylindrical lenslets 93. The two arrays are crossed suchthat the axes of the cylindrical lenslets on the arrays are orthogonalor perpendicular to each other.

Another alternate embodiment is a screen comprised of reflective concavelenslets. This concept is shown in FIG. 34(a). Alternatively, reflectivecorner cubes can be used as shown in FIG. 34(b). The elements can bespherical lenslets that are hexagonally close-packed, or the carvedequivalent of crossed cylindrical lenslets, or corner cubes, or justplain cylindrical lenslets arranged horizontally with their axesvertical for the elimination of vertical parallax. The method ofprojection using this screen is shown in FIG. 35. A color plate is shownfor reproduction of color images from black-and-white film.

Another alternate embodiment would be to have a screen consist of a zoneplate matrix lens array. This concept is shown in FIG. 36. This screenwould consist of a zone plate matrix array 94, each zone plate havingalternating different focal lengths for their respective alternatingmonochrome colors. A color plate 95 would be necessary in this case. Theimage would then be focused onto a focal plane 96 as shown.

Another alternate embodiment shown in FIG. 37 is a zone plate screenconsisting of horizontally arranged cylindrical zone plates 97 arrangedso that their axes are vertical along with a color plate 98 consistingof vertical strip filters of alternating colors. The focal lengths ofthe zone plates are different and are allied respectively with themonochrome colors of the associated color plate. A diffusing screen 99is located at the focal plane of the zone plate and color plate arrays.The primary portion of the screen is a flat plate onto which is drawnparallel vertical lines which can separate the plates into a series ofzones. For each zone plate, the lines are drawn a distance r_(n) apartsuch that equations [11] through [14] hold true for the horizontaldirection. Once again, the vertical lines are grooves which make up thecylindrical zone plates, can be produced either mechanically,photographically or holographically. When using a cylindrical zone platescreen, the color plate is not optional. It is required due to thesevere chromatic selectivity of a zone plate.

The final alternate embodiment, shown in FIG. 38 for the screen consistsof a large Bonnet Screen 100 an associated color plate 101 and adiffusing screen 102.

The discussion now turns to the concept of projection. The theoreticalconcept of projection is really quite simple. It consists of two stages.In the first step, shown schematically in FIG. 39, the multiplexedimages 103 must be separated into rows 104; then, each row in 104 mustonto the screen in its proper position, horizontally adjacent to thenext row. In this second step, the magnification in height is muchgreater than that in width. Therefore, a highly anamorphic system mustbe used. FIG. 40 is an optical ray trace that illustrates this secondstep design. To properly design a simple projection system, thefollowing procedure should be used. Known is the size of the frame y′,the size of the image on the screen, y, and the distance, s, of theprojector lens from the screen. The magnification of the projected imagefor the lens is y/y′. This magnification factor can also be expressed asthe ratio of the distance of the two images from the lens s/s′.

Therefore, $\begin{matrix}{{M = {\frac{s}{s^{\prime}} = \frac{y}{y^{\prime}}}},\quad {{{and}\quad s^{\prime}} = \frac{{sy}^{\prime}}{y}}} & \lbrack 42\rbrack\end{matrix}$

We also know that $\frac{1}{f} = {\frac{1}{s} + \frac{1}{s^{\prime}}}$$f = \frac{{ss}^{\prime}}{s + s^{\prime}}$

Substituting equation [42] into this expression for ƒ, we have:$\begin{matrix}{f = \frac{{sy}^{\prime}}{y + y^{\prime}}} & \lbrack 43\rbrack\end{matrix}$

Now, for our example, for the X-direction

s=W  [44]

where:

W is the width of the screen, and

is the factor indicating the size of the audience.$y = {{{W/\#}\quad {rows}\quad {and}\quad \# \quad {rows}} = {{\frac{n\quad \varphi}{y^{\prime}}\quad {and}\quad y^{\prime}} = w}}$

where w is the width of the frame.${{Then}\text{:}\quad y} = \frac{Ww}{n\quad \varphi}$

Substituting these terms in equation [42], we have

s′ _(x)=nφ  [45]

Similarly, using equation [43], $\begin{matrix}{f_{x} = \frac{\wp \quad {Wn}\quad \varphi}{W + {n\quad \varphi}}} & \lbrack 46\rbrack\end{matrix}$

where:

n=number of elements

φ=diameter of camera lenslet.

Using the same method for the Y-direction,

s=′W and y=W/2

(The total magnification of the element in the height direction is tobring it to the total height of the screen. For our examples, the screenis twice as wide as it is high.).

From equation [42], we have: $\begin{matrix}{{s_{y}^{\prime} = {\frac{{\wp \quad}^{\prime}{Wy}^{\prime}}{W/2} = {2\quad \wp^{\prime}\quad y^{\prime}}}}{{{In}\quad {this}\quad {case}},\quad {y^{\prime} = {\delta = {\frac{h}{\# {rows}} = {{\frac{hw}{n\quad \varphi}\quad s_{y}^{\prime}} = {\frac{2\quad {\wp \quad}^{\prime}{hw}}{n\quad \varphi}\quad {and}}}}}}}} & \lbrack 47\rbrack \\{f_{y} = {\frac{2\quad \wp^{\prime}\quad {hWw}}{{n\quad \varphi \quad W} + {2{hw}}}\wp}} & \lbrack 48\rbrack\end{matrix}$

Let us choose an example.${{\varphi = {1.0\quad {mm}}},\quad {\delta = {\frac{hw}{n\quad \varphi} = {4.81\quad {mm}}}},\quad {n = {1,756}},\quad {h = {130\quad {mm}}},{w = {65\quad {mm}}},\quad {W = {10,000\quad {mm}}},\quad {\wp = 6.}}\quad$

Now, from equation [44], s≈60 meters, and from equations [45] through[48], we have:

ƒx=8.97 meters

s′_(x)=10.53 meters

′=7.

ƒ_(y)=6.73 meters

s′_(y)=67.3 mm

An anamorphic lens of this type is highly unlikely, and the concept ofprojection is not as simple as it looks on the surface. For a thoroughanalysis of the projection system, the problem must be divided into thefollowing sections:

(1) Primary Projection System

The resolution of the film and its image will range between 300-500lines/mm. There is no projection lens in existence which can projectsuch a high resolution image from a small frame onto a large screen.Therefore, a projection system must be devised to project the image witha reasonable magnification so as to enable a more standard projectionsystem to project the image on the screen.

(2) Image Multiplexing System

(3) Image Inversion

The picture taken by the camera, when projected, will have apseudoscopic three-dimensional reconstruction. It is necessary to invertthis three-dimensional image so as to create an orthoscopicreconstruction. This concept will be discussed in detail later. Onemethod of performing this operation is projecting the pseudoscopicreconstruction and photographing the reconstruction on an integralphotograph or a hologram. The new reconstruction will be orthoscopic.However, this process introduces a theoretical resolution loss factor of{square root over (2)}. Should it be possible to perform this functionin the projector without necessitating an intermediate reconstruction,it would be possible to avoid this loss in resolution.

(4) Secondary Projection System

A projection system must be devised which will project the magnifiedimage from the primary system onto the screen. This projection systemwill be highly anamorphic.

(5) Registration System

A method must be devised which can register the projected images(intermediate and final) exactly where they should be on theirrespective image planes. The focal position must also be registered.

(6) Illumination System

(7) Mechanical Registration System

(8) Mechanical Stabilization System

The primary projection system does not include the optics for projectingthe integral photographic image onto the screen. Instead, it is requiredto magnify the high resolution film format to some intermediate stagewhile maintaining the same number of resolution elements so as tofacilitate theater projection using more standard optics.

The function of the primary lens is simply the aforementionedpreliminary magnification. First, the lens must have the requiredresolution or$\frac{1}{R} = {2.44\quad \lambda \quad \left( {F/\#} \right)}$$\left( {F/\#} \right) = \frac{1}{2.44\quad \lambda \quad R}$

For our example, λ=5,000 Å=0.5×10⁻³ mm and R=400 lines/mm.

Therefore, (F/#)=2.05.

This means that any F/2.05 lens, even a simple one, would provide aresolution of 400 lines/mm in the center of the field. A small lens,such as one used as a lenticule to take an integral photograph possessesthe ability to resolve 400 lines/mm over the entire field. However, thefield of such a lenslet is very small, and the light gatheringcharacteristics for this lens is very poor.

Second, this high resolution must be maintained over the entire field ofthe film (i.e., 65 mm×130 mm) without distortion or abberation. Thedesign of such a lens is not simple, and it will not be included in thisapplication. However, lenses with characteristics similar to thatrequired by this system already exist and designing such lenses is wellknown to those familiar with the art. The lens which must be used forthe primary projection must be designed using a computer. It will havebetween 10 and 15 elements. The depth of focus required to maintain thetotal information of the projected image is very poor. However, this ismuch more controllable when projecting to an intermediate magnificationthan on a large screen.

A special case of this intermediate projection is when it is performedat no magnification. This will prove useful in certain of the finalprojection systems which will be described later. What is required isthat an image be transferred from one image plane to another at 1:1magnification with the resolution preserved, i.e., the total informationmust be transferred from one image to the other. In order to accomplishthis, a special optical system must be designed, but such an opticalsystem is much simpler than the one previously mentioned. One suchsystem was designed by PERKIN-ELMER several years ago. This opticalsystem uses mirrors instead of lenses, but there are not a great numberof components, and the components are not difficult to construct. Suchan imaging system was designed for a microprojector and semiconductorcircuits. It covered a field of two-inches. Resolution was one-micron or500 line pairs/mm. Of course, lenses can be used to accomplish the sameresult. However, the optical system as a whole is an extremely practicalone.

Another way to accomplish the primary projection is to use holography.FIG. 41 shows the basic principle of holographic primary projection. Theimage from the film 105 is projected, using lens 106 onto a hologram 107which is designed to project the real image of the film onto thesecondary image plane 108 at a suitable magnification. Coherent lightmust be used as the illuminating source in this case if perfect imageryis to be obtained. FIG. 42 shows a method which is currently used toproject a real image from a hologram. A hologram 109 which is taken as apermanent record of the object to be reproduced is illuminated usingcoherent light 110. A real image is projected from the hologram 109 ontothe secondary image plane 111. The figure shows this being accomplishedusing a reflection hologram, but transmission holograms would work justas well. Once again, coherent light must be used for perfect imagery. Inthe manner shown, an image can be projected at a 1:1 magnification witha resolution of 650 lines/mm. Should incoherent light be used, the imagewould degrade to approximately 500 lines/mm. For perfect imagery, unitmagnification should be used, even though holographic images can bemagnified, but not without abberation. This 1:1 projection is used inmicroprojectors in the semiconductor industry. The problem with thismethod is the need for preparing a permanent hologram for each frame forprojection, i.e., the film would have to be a hologram. (This techniquewill be discussed later.) The 1:1 magnification would not present aproblem since the object in the hologram can be made quite large (i.e.,the size required for primary projection). Reflection holography shoulddefinitely be used since the diffraction efficiency is much higher thanfor transmission holography. FIG. 43 shows how a non-permanent image canbe projected using the principle of primary holographic projection. Thetwo-dimensional image from the film 112 is projected onto a reflectionhologram 113 using a 1:1 imaging optical system 114. The image is thenfocused onto a secondary image plane 115. In this case, a speciallydesigned abberation free lens 116 is used in conjunction with thehologram for projection. Since this expensive lens must be used duringnormal projection of the film, this method is not very practical.However, since a hologram is an imaging device itself, the hologram canbe used as a high quality lens.

FIG. 44(a) illustrates this principle. A standard projection lens 117images the film frame 118 onto a specially prepared hologram 119, which,in turn, acts as a reflecting lens to image the film frame onto thesecondary image plane 120 at some greater magnification. This hologramis a high quality Leith Hologram, and is indicated operating as areflection hologram because the diffraction efficiency is much higherfor reflection than for transmission. FIG. 44(b) shows how such aholographic lens can be made. For the reference beam 121, one shouldproject the image of an aperture 122 which is the size of the film frameonto the photographic plate 123 using the same projection lens 124 aswill be used in the projector. This lens 124 does not have to be of highquality. A diffuser plate 125 should be used as shown. For the objectbeam 126, one should project the image of a larger aperture 127, whichis the size of the magnified image, onto the photographic plate 123using an extremely high quality projection lens 128. Once again, adiffuser plate 129 must be used as shown. The advantage of this methodover the previously mentioned methods is the elimination of theexpensive high quality lens during projection. This lens 128 only needbe fabricated once, and then it will be used to manufacture all of theholographic projection lenses.

Another method of accomplishing the primary projection by holographicmeans, but without the use of an expensive lens, is illustrated in FIG.45. In this method the entire frame 130 is not imaged as a whole fromthe film onto the secondary image plane 131 using a hologram, but,rather, each individual element is imaged using each lens from a matrixlens array 132 in the same manner as is shown in FIG. 43. This method isillustrated in FIG. 45. Once again a 1:1 imaging system 133 is used toproduce an unmagnified image of the film frame 130 onto reflectionhologram 134. This image is then reconstructed onto the secondary imageplane 131 using the matrix lens array 132. Since the individual lensesin the matrix lens array 132 have the ability to perform high qualityprojection imaging of each element, it is no longer necessary tofabricate the expensive, high quality lens. In this instance, the matrixlens array 132 will be used for projection in conjunction with theholographic lens. This configuration would probably be of more utilitywith transmission holograms, even though the principle is illustratedhere for reflection holograms.

Another method of accomplishing projection using a holographic imagingdevice is shown in FIG. 46. This is the preferred embodiment of theprojection system. In this case, instead of using expensive projectionlenses, two matrix lens arrays, 135 and 136, are used as shown. On thesecondary image plane, the image is magnified by the desired amount, andthe ratio of the size of the elements of matrix lens array 136 to matrixlens array 135 is equal to the magnification. The hologram is preparedas follows. In the setup shown in FIG. 46, replace both the film 137 andthe secondary image plane 138 by two diffuser plates. Between the filmplane diffuser plate and matrix lens array 135, place a movable aperturewhich is the size of one element on the film frame 137, and between thesecondary image plane and matrix lens array 136, place a similar movableaperture which is the size of a magnified element on the secondary imageplane 138. A high resolution photographic plate is positioned in thehologram plane 139. The film plane aperture is placed in front of thefirst elemental position and the secondary image plane aperture isplaced in the corresponding first elemental position. Both diffuserplates, 137 and 138, are then trans-illuminated by an appropriate laserfor a sufficient time to expose the hologram 139. (This may have to bedone for each element by exposing it with many bursts of low intensitylaser radiation.) Both apertures are then moved to the second elementalpositions and the hologram is exposed again; and so-on for everyelemental position. Another method of preparing the same hologram is toalso place an appropriate elemental aperture in front of the hologramplane 139. This elemental aperture moves to a different position infront of the hologram plane every time the other two apertures move. Theaddition of this third aperture will avoid reciprocity problems with thephotographic emulsion. (Reciprocity problems will also be avoided by theshort-burst method mentioned above. The advantage of the short-burstmethod over the third aperture method is that crosstalk between elementsis avoided.) This method of projection using holographic imaging seemsto be the most practical embodiment of the projection principle.

Holographic lenses and imaging devices have the major advantages overconventional optics in that holograms use less expensive fabricationprocedures and fewer elements are needed to produce an abberation freeand distortion free image. Its major disadvantages lie in the fact thatprocessing is difficult (during wet processing, a photographic emulsionwill usually shrink—a phenomenon which must be prevented here), and thatcoherent light must be used during projection (except, as will be seen,for the method outlined in FIG. 46). However, the advantages may proveto outweigh these disadvantages.

Another method of accomplishing the primary magnification and analternate embodiment is by direct magnification instead of by primaryprojection. This can be done using a fiber optics magnifier, a devicewhich is fabricated from a fiber optics cone. The light from the imageis not only transmitted from one surface to the other by the fiberbundle, but, since the fibers are smaller at one surface than they areat the other, magnification or demagnification can occur depending uponwhich surface is in contact with the primary image. FIG. 47 illustratesjust how such a fiber optics magnifier can be fabricated. A large fiberoptics boule is suspended in a vertical cylindrical furnace such thatone end will become sufficiently molten so that it can be pulled into acone. For fabricating two cones, a bundle of fibers is hung in a smallfurnace and fairly intense heating is applied to the middle of theboule, which when softened, is drawn apart. However, unless the thermalconditions are completely symmetrical, the cone is deformed.Furthermore, after the cones are pulled, they must be annealed orconsiderable strains and fractures occur. The appearance of the twocones is shown in FIG. 47(a). The cones should be fabricated in a vacuumso as to prevent air from becoming encapsulated in the fibers. The conethat is to be used is then truncated and two faces are polished. This isshown in FIG. 47(b). From this point on, the fiber optics cone is cutinto the shape of a truncated pyramid in such a way that one face is thesize of the film frame and the other face is the size of the magnifiedimage. This is shown in FIG. 47(c). Another way to fabricate the conewould be out of metal tubing. Once the fiber optics magnifier isfabricated, FIG. 48 illustrates how it can be used. The primary faceplate of a fiber optics magnifier 143 is in contact with the film 141.The unmagnified image 140 on the film 141 becomes a magnified image 142on the secondary face plate of the fiber optics magnifier 143.

The advantage of a fiber optics magnifier is that if the fiber opticscone is symmetrically formed, there will be no abberations. However,with fibers whose diameters are as small as these must necessarily be,there will be many fractures in the fibers. This will serve to reducethe resolution. This problem can be solved by using metal fibers.Another disadvantage occurs due to the fact that original multiplexingof the film in the camera was performed using a fiber optics imagedissector. Because of this, there will be a resolution loss due tocoupling of two fiber optics surfaces. This can be expressed as follows:$\begin{matrix}{R^{\otimes} = \frac{R_{1}\sqrt{2}}{2}} & \lbrack 49\rbrack\end{matrix}$

where:

R₁ is the film resolution, and

R^({circle around (x)}) is the maximum resolution which can betransferred by a fiber optics bundle whose two faces are the same size

Equation [49] indicates a definite loss of information uponmagnification.

Image unmultiplexing and inversion must now be discussed. FIG. 49illustrates the concept of unmultiplexing. The fully multiplexed film isshown in FIG. 49(a). This is the image as it appears on the finalprocessed film prior to projection. The first step which must beaccomplished is the separation of the vertical rows for projection. Thisis shown in FIG. 49(b). As long as the adjacent rows are positioned sothat they are touching one another, they cannot be projected separatelyto different positions relative to each other. Therefore, thisseparation step is necessary. The second step of the process is theprojection or positioning of the vertical rows side-by-side horizontallyso that they may be in the same order as they were when the photographwas originally taken before the multiplexing step in the camera. This isshown in FIG. 49(c). The final step (which can be accomplished duringthe final projection) is magnification in the vertical direction so asto bring the dimensions in the vertical direction into correctproportion when the three-dimensional image is produced. This is shownin FIG. 49(d).

The first step of separation can be accomplished either with the use ofprisms (or mirrors) or the use of fiber optics. The former method mustimply a multi-faceted prism of the type shown in FIG. 50, each facedirecting light in a different direction, one face corresponding to eachvertical row. Fiber optics can be particularly useful for accomplishingthis step, especially since the initial image upon which it is operatingis magnified, and, therefore, possesses a reasonably low resolution.

The second step, which is the actual unmultiplexing step (placing thevertical rows side-by-side horizontally), can be accomplished byprojection with lenses or by proper positioning with fiber optics. Inthe former method, at least one lens must be used to project each row,but more lenses can be used. A particular embodiment of this techniquewould be the fabrication of a combination lens, similar to a matrix lensarray, having all the necessary directional lenses mated together in onestructure. Using the latter method, both steps 1 and 2 can be combined.What would be needed here would be a fiber optics image dissector of thetype shown in FIG. 6, a similar device which was used for the originalmultiplexing.

By far, the most practical method and the preferred embodiment ofunmultiplexing is with the use of a holographic imaging device. Not onlycan the entire image unmultiplexing process be accomplished in one stepusing such an element, but so also can both the inversion of the imagefrom pseudoscopy to orthoscopy and the final projection (if these stepsare desired to be performed using this method). The utilization of theholographic imaging technique to perform these latter two functions willbe discussed in the next two sections. The use of this method is shownin FIG. 51. The magnified image from the secondary image plane 144 isprojected onto a specially prepared hologram 145, using a standardprojection lens 146. The hologram is so designed that when illuminatedwith such a reference beam, it will generate an object beam which whenprojected through a second projection lens 147, will image onto anotherplane a picture having the vertical rows arranged side-by-sidehorizontally 148. (It will be shown later that it is highly desirable toreplace the projection lenses by two matrix lens arrays.) The method tofabricate such a hologram can be illustrated using FIG. 51. Replace thesecondary and unscrambled image planes (144 and 148 respectively) bydiffusing screens. Apertures must be used with both reference and objectbeams so as to direct the location, size and shape of each correspondingrow between the secondary and unscrambled image planes. This holographicimaging device is then fabricated by the same method as that which isshown in FIG. 46 as previously described. (This is not to say that theholographic imaging device described here is the same as previouslydescribed and illustrated in FIG. 46, but only that it is fabricated ina similar manner.) Similarly, as with the previous holographic imagingdevice, an aperture could be used with the photographic plate to solvethe problem of emulsion reciprocity, or the short-burst method can beused.

A necessary step in either film processing or in projection is theinversion of the three-dimensional image from pseudoscopy to orthoscopy.Any integral photograph projected by the standard method to produce athree-dimensional image will also project a pseudoscopic image (i.e.,three-dimensionally, the image will appear inside out). The standardmethod of inverting a pseudoscopic image is to reconstruct thethree-dimensional image in the usual manner and then to re-photographthe reconstruction with a second camera. The reconstruction of thissecond film will produce a pseudoscopic image of the three-dimensionalimage which was photographed. Since, this image was originallypseudoscopic, the pseudoscopic reconstruction of this image would beorthoscopic. This method of image inversion is shown in FIG. 52. Thistechnique has two major disadvantages. First, an intermediate processingstep is required in which a second film must be made; second, there isan inherent resolution loss of {square root over (2)} when going fromone film to the other.

There is another basic method of producing orthoscopic images frompseudoscopic images which will not incur this resolution loss. Thismethod is new and novel. The basic principle is quite simple. Referringto FIG. 53, if the film format shown in FIG. 53(a) produces apseudoscopic image, then it can be shown by an optical analysis of whata second film record would look like were three-dimensional image fromFIG. 53(a) to be photographed, that the film format of both FIGS. 53(b)and (c) would produce an orthoscopic mirror image of the pseudoscopicthree-dimensional image produced by the format of FIG. 53 (a), whileformat of FIG. 53(c) will produce a correct orthoscopic image.

The method for image inversion which is to be discussed here willconcern itself only with its performance in the projector. Anyintermediate processing where another film must be prepared will bediscussed in a later section. The proposed method is to perform thisinversion during unmultiplexing when a holographic imaging device isused (refer to FIG. 46). In this case, each element would be mirrorimage inverted, but the order of the elements could be kept in-tactholographically. In fact, the elements can be holographically arrangedin any order that is desired.

Holographic imaging devices can be used with more-or-less standard,inexpensive lenses to accomplish all projection functions. FIG. 54 showsthe final schematic configuration of this type of projector. Thisrepresents the preferred embodiment of the optics of the holographicprojector. The image on the film 149 is first magnified onto a secondaryimage plane 150 holographically using two matrix lens arrays, 151 and152, by the concept shown in FIG. 46. This magnified image is then usedas the reference beam for the second hologram 153 so as to reconstruct amagnified, unmultiplexed, inverted image on the unscrambled image plane154. This unscrambled image plane can either be an intermediate plane orthe screen itself. In the configuration shown, it is an intermediateplane, and a position adjustable projection lens 155 is used to projectthe image formed at this plane onto the screen. No diffuser plates areneeded at the intermediate image planes (although they can be used ifnecessity dictates), and their use is undesirable since they add greatlyto the required illumination levels. The only non-holographic opticalelements in the projector are either simple projection lenses or matrixlens arrays. Therefore, the holographic projector represents a farsimpler system than the projector using more conventional optics.

The secondary projection system will now be discussed. The finalprojection lens should be basically defined by equations [45], [46],[47] and [48], where h and w are the dimensions of the image on thesecondary image plane. However, the magnification of this system in thehorizontal direction is very close to one. This means that thehorizontal element of the projection lens must be positioned midwaybetween the projector and the screen. This is highly impractical.

In actuality, the ratio of the magnification in the vertical directionto that in the horizontal direction is 18.28:1. As an example, for aten-meter wide screen, the vertical magnification is 104 while thehorizontal magnification is 5.69. FIG. 55(a) shows the arrangement forprojection of an image by a simple projection lens. h_(o) represents theobject whose image is to be projected while h_(i) represents theprojected image itself. For simplicity, the object to be projected isrepresented by an arrow, and, therefore, so also is the projected image.ƒ is the focal length of the lens, and s and s′ represent the distancesof the lens from the object and image planes respectively. Themagnification M is given by:$M = {\frac{h_{i}}{h_{o}} = \frac{s^{\prime}}{s}}$

Obviously, if (s+s′) is large, as it would be in a large movie theater,and if, in addition, the magnification is small, then the lens must beplaced at a great distance away from the object or film plane. This ishighly impractical.

An alternative lens system for the horizontal direction to that justdescribed is shown in FIG. 55(b). The lens system shown here will directall rays from the object plane to the image plane, and yet, will belocated close to the object plane, thereby making it possible to projecta low magnification image in a theater situation. FIG. 56 schematicallyillustrates just such a lens example. This lens system is a basic threecylindrical element, anamorphic lens system. The first lens, a positivecylinder, serves to magnify in the vertical direction, while the secondtwo lenses, a negative plus a positive cylinder, serves to magnify inthe horizontal direction. The screen is ten meters wide by five metershigh, and the theater is approximately sixty meters long. The dimensionsof the lenses along with their focal lengths are shown in the figure.The horizontal magnification is 5.69 while the vertical magnification is99.0.

The exact design of this lens system is not included here. Even were theexact system described in FIG. 56 to be needed, the lens system shown inthe figure only indicates a first order solution. To reduce abberationand distortion, each lens in the optical system is, in itself, amulti-element lens. Therefore, approximately a dozen lenses will berequired in this lens system. Even though this lens is a complex opticalsystem, it is possible to use such a lens to adequately project thehighly anamorphic image onto the screen.

As has been mentioned many times before, it is essential that theprojected image be registered on the screen to very close tolerances.This registration must be performed in three directions: the horizontaland vertical directions and the focus. Registration in the horizontaland vertical directions can be best accomplished by using Moiré Patternscreated by circular bulls-eyes. One bulls-eye would permanently beaffixed to the screen, and a second would be projected onto the screenby the projector. Both bulls-eyes, when superimposed on each other onthe screen, will be the same size. Should the images be misregistered, aMoiré Pattern would appear. When the Moiré Pattern disappears, theprojector is positioned so that the projected image is properlyregistered on the screen. An electronic servo-mechanism would insureproper registration by this method.

To insure proper focus, several automatic focusing devices can be used.Such a device could be a cadmium sulfide (CdS) photocell with indium(In) electrodes. Should this automatic focusing device be positioned onthe screen, and should a portion of the image be projected onto thisdevice, an electronic signal would insure that the image is properlyfocused.

The same techniques which are used to register and focus the image onthe screen, can also be used for the intermediate image planes withinthe projector.

The illumination system will now be discussed. The brightness of animage viewed from the screen depends upon the size of the theater, and,therefore, from our human engineering considerations, the size of thescreen. For a 10×5 meter screen, whose area is 538 square feet, thebrightness of the image should be 867 foot-lamberts.

The screen is divided into alternating red, green and blue verticalzones. 18.82% of the spectrum of the incident light is used for the redportion of the image, 38.2% is used for green and 13.18% for blue. Sincethese vertical elements are so small as not to be resolved, there is asumming of these colors, and the efficiency can be averaged at 23.4%.This means that whenever color images are produced from black-and-whitefilm by an additive process of three colors, the image brightness isonly 23.4% of what it would have been by a standard color projectionprocess. (This statement also holds true for the standard methods ofproducing color television pictures.)

Since the most preferred configuration of the screen is to construct itas a reflection hologram, as is shown in FIG. 31, the diffractionefficiency (conservatively speaking) should be approximately 80%. Theoverall efficiency of our three-color holographic screen is, therefore,18.7%.

The incident illuminance must be 867÷0.187 or 4,630 foot-candles×538square feet or approximately 2.5-million lumens. To calculate theoptical system efficiency, assume that 70% of the light is collected bya very efficient condenser, and that 80% of the light is transmittedthrough the condenser. Furthermore, assume that 85% of the light istransmitted through the film. To calculate the efficiency of theprojection system, assume an optical system for projection to consistof:

ELEMENT EFFICIENCY Matrix Lens Array #1 0.92 Hologram #1 0.80 MatrixLens Array #2 0.92 Projection Lens #1 0.85 Hologram #2 0.80 ProjectionLens #2 0.85 Projection Lens #3 0.85

This is the projection system shown in FIG. 54. The total projectionoptics efficiency is 0.333. Assume a 33.3% efficiency. Therefore, theoverall optical system efficiency is 15.85%.${{{TOTAL}\quad {FLUX}\quad {FROM}\quad {SOURCE}} = {\frac{2.5 \times 10^{6}}{0.1585} = {1.575 \times 10^{7}\quad {lumens}}}},$

or 15-million lumens.

The brightest source of incoherent illumination is the carbon arc. Rodsof carbon from 6-12 inches in length and from ¼-inch to ½-inch indiameter are placed either horizontally, as shown in FIG. 57(a), or atan angle, as shown in FIG. 57(b). FIG. 57 shows two types of carbonarcs:

(a) with condensing mirror for moderately sized motion picture theaters,and

(b) with condensing lenses for large motion picture theaters.

Sometimes, the carbon rods are copper coated to improve electricalconductivity. To start a carbon arc, the two carbons are connected to a110-V or 220-V DC source, are allowed to touch momentarily, and are thenwithdrawn. Intense electron bombardment of the positive carbon causes anextremely hot crater to form at the end of the positive carbon. Thisend, at a temperature of approximately 4,000° C., is the source oflight. An electric motor or a clockwork mechanism is used to keep thecarbons close to each other as they burn away. Carbon arcs are used inall motion picture theaters, where they operate on from 50 to severalhundred amperes. Extremely high intensity carbon arcs use much electricpower, generate much heat and must be water cooled.

We now turn to an analysis of the problem of picture jitter on thescreen and stabilization. Previously, when discussing the camera design,a specific analysis was performed for misregistration due to motion ofthe film. The requirements for stabilization and methods forimplementing strict film registration were discussed. At this point, are-analysis of the problem will be performed with emphasis on theprojector motion. FIG. 58(a) shows the effect which misregistration of apoint on the screen has on the three-dimensional virtual image. A is thescreen onto which the projector image is focused, ƒ_(s) is the focallength of the screen lenticules, and B is the central plane of thescreen lenticules. (For a front projection, B is the central plane ofthe focal points of the cylindrical elements.) Y is the distance of thethree-dimensional virtual image of the point P from the screen. Shouldthe projected two-dimensional image of the point on the screen bemisregistered by a distance Δx, the virtual image of point P will bemisregistered by a distance Δ P. Referring to FIG. 58(b):$\frac{\Delta \quad x}{\Delta \quad P} = \frac{f_{s}}{Y}$

In the case of the holographic front projection screen:$\frac{\Delta \quad x}{\Delta \quad P} = {\frac{f_{s}}{f_{s} + Y} \approx \frac{f_{s}}{Y}}$

Now, referring to FIG. 58(c), we can see the maximum misregistration ΔP.The viewer closest to the screen is positioned at the apex of thetriangle, and V is the distance of this viewer from the screen.

ΔP=(V+Y)α

where α is the angle of minimum visual acuity. Substitute thisexpression in the previous one, we obtain:${\Delta \quad x} = {{\frac{f_{s}}{Y}\Delta \quad P} = {{\frac{f_{s}\alpha}{Y}\left( {V + Y} \right)} = {f_{s}\alpha \quad \left( {\frac{V}{Y} + 1} \right)}}}$

Let V=EW

where W is the width of the screen, and E is a factor indicating theminimum distance at which a viewer can be from the screen. Therefore:${{But}\quad \Delta \quad x} = {{f_{s}{\alpha \left( {\frac{EW}{Y} + 1} \right)}\quad \frac{f_{s}}{f_{c}}} = {{\frac{W}{n\quad \varphi}\quad f_{s}} = {\left( \frac{f_{c}}{n\quad \varphi} \right)W}}}$${{Let}\quad K} = {\frac{f_{c}}{n\quad \varphi} = \frac{\left( {F/\#} \right)}{n}}$

K is a characteristic of either the camera or the screen. Therefore,$\begin{matrix}{x = {{KW}\quad \alpha \quad \left( {\frac{EW}{Y} + 1} \right)}} & \lbrack 50\rbrack\end{matrix}$

Δx is the maximum tolerable lateral movement of the projector. To findthe minimum allowable Δx, we must look at the point in space upon whicha small deflection Δx would have the greatest effect ΔP. Such a pointexists where Y is at infinity. Therefore, the minimum allowable lateraldeflection is:

$\begin{matrix}{{\lim\limits_{Y\rightarrow\infty}{\Delta \quad x}} = {{KW}\quad \alpha}} & \lbrack 51\rbrack\end{matrix}$

Referring to FIG. 58(d), we can calculate the maximum tolerable angularmovement:$\in {= {f_{s}\alpha \quad \left( {\frac{E}{\wp \quad Y} + \frac{1}{\wp \quad W}} \right)}}$

where is defined by equation [44] and s is defined in FIG. 58(d).$\begin{matrix}{\in {= {{{\frac{f_{s}\alpha}{\wp}\left( {\frac{E}{Y} + \frac{1}{W}} \right)} \in} = {\frac{K\quad \alpha}{\wp}\quad \left( {\frac{EW}{Y} + 1} \right)}}}} & \lbrack 52\rbrack\end{matrix}$

Once again, the minimum allowable angular movement is given by:$\begin{matrix}{{\lim\limits_{Y\rightarrow\infty} \in} = \frac{K\quad \alpha}{\wp}} & \lbrack 53\rbrack\end{matrix}$

To perform a typical calculation, assume: (F/#)=1.7, n=1,734, W=10meters=10,000 mm, =6, and α=2.91×10⁻⁴ radians. (It will be shown laterthat for objects at infinity, this angle is much larger by a factor ofn/Rφ, where R is the resolution of the film.) R=400 lines/mm and φ=1 mm.Therefore, α=1.262×10⁻³ radians. K=9.8×10⁻⁴. Δx_(min)=1.237×10⁻² mm orapproximately 12 microns or 0.0005 inches. ε_(min)=2.06×10⁻⁷radians=3.28×10⁻⁶ arc-seconds.

Lateral sideways motion can be eliminated, or reduced to the desired0.0005 inches by firmly anchoring the projector, and making it moremassive. Most of the machine produced vibrations will not orientthemselves in this direction. Rotation around both the X-and Z-axes(refer to FIG. 16) can be eliminated both by firmly anchoring theprojector and by placing a gyroscope along the Y-axis. This firmanchoring can be accomplished by building a massive concrete table forthe projector with the center of the lens positioned directly above thecenter of gravity of the table. Because no integral imaging is performedin the vertical direction, vibrations causing vertical translation arenot important. Forward translation will cause a noncritical defocusingof the image. Finally, after the aforementioned steps are taken toeliminate motions in all of the indicated directions, the one remainingdirection, namely Y-axis rotation, will automatically be taken care of.

Using the previous theoretical analysis to calculate the minimumallowable film motion: $\begin{matrix}{{\frac{\Delta \quad x_{\min}}{\Delta \quad F_{\min}} = \frac{W}{n\quad \varphi}}{{\Delta \quad F_{\min}} = {\left( \frac{n\quad \varphi}{W} \right)\quad \Delta \quad x_{\min}}}} & \lbrack 54\rbrack\end{matrix}$

In our example, (nφ/W)=0.1734, and, therefore,

ΔF_(min)=2.15 microns.

This is easier to maintain than the one-half micron figure generated inprevious theoretical analysis for the camera. However, it must beremembered that the value for α used in equation [51] is a factor of4.34 greater than that used to evaluate equation [33]. The previouslydescribed film motion mechanism used in the camera, and shown in FIG.24(a), (b) and (c) can be used in the integral photograph projector.This mechanism can easily maintain film registration to the desired 2.15microns.

The discussion now turns to the use of a projector designed to projectmagnified three-dimensional images from holograms.

It is well known that when a hologram is projected onto a screen in theconventional manner, its ability to reconstruct an image is lost. Thisis so because the diffracting properties of the surface or volume of thehologram are needed for image reconstruction, and projecting a hologramonto a screen would only produce a picture of light and dark lines onthe screen. It is also well known that when a hologram is magnifiedphotographically, its reconstructed image is demagnified. Therefore, a70 mm hologram which is magnified to normal screen size, would producean image so small as not to be seen except with a microscope.Furthermore, it is known that when a three-dimensional image ismagnified, the magnification occurs disproportionately so that the depthmagnification is equal to the square of the magnification in the lengthand width directions.

It would appear from the above discussion that the three-dimensionalimage reconstructed from a hologram cannot be magnified for displaybefore a large audience. However, it is possible to apply the basicmethod of magnification and projection (as is used in the earlier partof this application for integral photographs) even to holograms. Theentire key to the process is the conversion of the holographic image toa two-dimensional integral photograph. Once such an integral photographis produced, it will not be difficult to magnify the three-dimensionalimage by the methods shown in previous discussions. What follows is,therefore, a discussion of the various methods of producing an integralphotograph from a hologram, suitable for magnification. The methodsdiscussed here are not expected to be all-inclusive, and are to be takenas examples only.

For the method of direct integral photography of a holographic image,the three-dimensional image is reconstructed from a holographic film.This image may either be real or virtual. A matrix lens array producesthe real-time integral photographic image of the object on a diffusingplate (not absolutely necessary) so as to be suitable for magnificationand projection. FIGS. 59(a) and (b) show this method being applied toboth real and virtual images projected from the holographic film. InFIG. 59(a), a holographic film 156 is illuminated with a reference beam157 of coherent light. This causes the reconstruction of the realthree-dimensional image 158 in space. This image is then transformedinto an integral photograph using matrix lens array 159 on diffusingscreen 160. Theoretically, there can be another film on the focal planeof the diffusing screen. However, the advantage of this method is thatone can directly project the three-dimensional images from holograms fora large audience in a theater without an additional process. Forreconstruction of the image in the theater, one need only apply theimage reconstruction optics previously described on the other side ofthe diffusing screen. FIG. 59(b) shows a similar process for athree-dimensional virtual image reconstructed from a hologram. Onceagain, holographic film 161 is illuminated with a reference beam 162resulting in the reconstruction of the virtual image 163. An integralphotograph of virtual image 163 is reconstructed on diffusing screen 165using matrix lens array 164.

The discussion now turns to the creation of an integral photograph ofthe three-dimensional image from multiple two-dimensional projectionsfrom a hologram. When a laser beam is allowed to impinge on a hologram,a real image of the object is projected. However, this real image willbe representative only of that portion of the hologram upon which thelaser beam impinges. If the diameter of the laser beam is small enough,the projected image will be two-dimensional, and will be representativeof the entire object or scene as seen from a particular viewing angle.This is illustrated in FIG. 60(a). In the figure, optically unprocessedcoherent light 166 emanating from laser 167 impinges on a holographicfilm 168. This causes a two-dimensional image 169 to appear focused on adiffusing screen 170. The smaller the aperture of the coherent lightbeam 166, the more in-focus the image 169 appears. This projected image169 is equivalent to an element of an integral photograph. An apertureor waveguide placed by the hologram can effectively give the projectedelemental photograph the desired shape. FIG. 60(b) shows how many ofthese elemental photographs can be produced in this manner. In thefigure, several optically unprocessed coherent light beams 171 impingeon a holographic film 172 that is in contact with a wave guide 173. Thewaveguide is also in contact with a diffusing screen 174. The samenumber of two-dimensional images are produced on the diffusing screen174 as there are laser beams 171. This method requires the use ofseveral laser beams (as many laser beams are required as are elementalphotographs) impinging on the hologram. FIGS. 61(a) and (b) show howmany parallel laser beams can be produced using several birefringentcrystals. Materials such as Potassium DiHydrogen Phthalate (KDP) exhibitthe property of splitting a ray 175 into an ordinary ray 176 and anextraordinary ray 177 as is shown in FIG. 61(a). By using N crystals inseries, the length of each, δ, being equal to twice the length of theprevious crystal, 2^(N) parallel laser beams are produced from a singlebeam. FIGS. 61(c) and (d) show how, by the use of a specially designedprismatic wedge plate, a series of laser beams can be made to emanatefrom a point in space to impinge on the hologram. In FIG. 61(d),collimated coherent light beams 178 impinge on prismatic wedge plate179. This is the same device illustrated in FIG. 61(c). This produces aseries of laser beams that are focused at point 180. The same number ofbeams now diverge from the focal point 180 and impinge on hologram 181thereby causing a series of two-dimensional pictures to be projectedfrom the hologram. This projected image 169 is equivalent to an elementof an integral photograph. An aperture or waveguide placed by thehologram can effectively give the projected elemental photograph thedesired shape. FIG. 60(b) shows how many of these elemental photographscan be produced in this manner. In the figure, several opticallyunprocessed coherent light beams 171 impinge on a holographic film 172that is in contact with a wave guide 173. The waveguide is also incontact with a diffusing screen 174. The same number of two-dimensionalimages are produced on the diffusing screen 174 as there are laser beams171. This method requires the use of several laser beams (as many laserbeams are required as are elemental photographs). impinging on theholograrm FIGS. 61(a) and (b) show how many parallel laser beams can beproduced using several birefringent crystals. Materials such asPotassium DiHydrogen Phthalate (KDP) exhibit the property of splitting aray 175 into an ordinary ray 176 and an extraordinary ray 177 as isshown in FIG. 61(a). By using N crystals in series, the length of each,δ, being equal to twice the length of the previous crystal, 2^(N)parallel laser beams are produced from a single beam. FIGS. 61(c) and(d) show how, by the use of a specially designed prismatic wedge plate,a series of laser beams can be made to emanate from a point in space toimpinge on the hologram. In FIG. 61(d), collimated coherent light beams178 impinge on prismatic wedge plate 179. This is the same deviceillustrated in FIG. 61(c). This produces a series of laser beams thatare focused at point 180. The same number of beams now diverge from thefocal point 180 and impinge on hologram 181 thereby causing a series oftwo-dimensional pictures to be projected from the hologram.

The discussion now proceeds to holography of a two-dimensional integralphotographic film. In this method a holographic movie film is used.However, the projected real image of the hologram is a two-dimensionalimage which is projected onto a diffusing screen (or imaginary imageplane). This image is the integral photograph to be projected. Thisprocess is illustrated in FIG. 62. Since the initial photograph whichwill be taken by the camera is an integral photograph, a hologram can betaken of each frame of the integral photographic film, and thereconstructed image will, therefore, be the integral photograph.Referring to FIG. 62, to construct the hologram 182, a laser beam 183passing through a standard projection lens 184 serves as the referencebeam. The integral photographic frame is projected using the same laserbeam onto diffusing screen 186 which produces the object beam 187. Thecombination of reference beam 185 and object beam 187 produces thehologram. To reverse the process for projection, light impinges uponprojection lens 184 and then upon the holographic frame 182. Thisreconstructs object beam 187 that produces a focused image of theintegral photograph on diffusing screen 186. This method contrasts withthat of direct holography where holograms are taken of the scenedirectly. This latter method requires projection techniques as has beenpreviously discussed.

Just as holograms produced from two-dimensional integral photographs canbe fabricated, so can they be fabricated from composite two-dimensionalphotographs. This work is current state-of-the-art. FIG. 63(a) showsjust how such photographs can be taken with multiple cameras, C₁, C₂ ,C₃ , etc. The greater the number of cameras, the better the quality ofthe three-dimensional reconstruction. FIGS. 63(b) and (c) show methodsof converting these component photographs to a holograrm FIG. 63(b)shows this process for a single integral photograph. The photograph isprojected (focused) onto a diffuser plate 188 using coherent light 189.The same light produces reference beam 190. This exposes a portion ofphotographic plate 191 through a movable aperture 192. This isillustrated more completely in FIG. 63(c). FIG. 63(d) shows anothermethod of producing these component photographs. In this case, theobject 193 is photographed using incoherent illumination 194 (such asordinary white light). A movable aperture 195 allows a restricted viewof the object to pass through lens 196 exposing a picture onphotographic plate 197. FIG. 63(e) shows how to produce a hologram fromthese photographs. FIG. 63(f) shows how the hologram produced from thecomponent photographs of FIG. 61 can be reconstructed.

Reflection holograms can be used more conveniently for the followingreasons:

The diffraction efficiency is significantly higher.

Use of white light illumination is more convenient.

Color holograms are more easily produced.

Other than the differences between reflection and transmission hologramsfor positioning of the illumination with respect to the projected image,all arguments previously expressed for holographic projection oftransmission holograms hold true for reflection holograms.

In 1968, Dr. D. J. DeBitetto of Phillips Laboratories, Briarcliff Manor,N.Y., published several articles concerning holographicthree-dimensional movies with constant velocity film transport. In thesearticles, he described holograms produced which allowed bandwidthreduction by elimination of vertical parallax. This was accomplished bymaking the three-dimensional holograms on a film strip using ahorizontal slit as an aperture. The frames were formed by advancing thefilm each time by the width of the slit. Each frame was animated. Afterdevelopment, the film was illuminated as any hologram would be, and thefilmstrip was moved at constant velocity. I have seen Dr. DeBitetto'sholographic movies, and they are the best attempts to-date in the fieldof motion picture holography. The three-dimensional pictures are ofextremely high quality. However, vertical parallax was absent.

The same technique can by used in our projector. It can be used withdirect holography as Dr. DeBitetto did or it can be used with hologramsof integral photographs as shown in FIG. 64. In this figure, and by thistechnique, a horizontal strip hologram 198 is taken of each integralphotographic frame 199 (in any format, multiplexed or unmultiplexed),and the holographic film strip is advanced for each frame. This is doneby projecting the integral photographic frame 199 onto a diffuser plate200 using coherent illumination from a multicolor laser 201 (e.g, awhite light krypton laser). This becomes the object beam necessary toproduce the hologram. It is possible to take several strip holograms ofthe same frame. Afterwards, the holographic film 202 is played back inthe projector at constant velocity.

Dr. DeBitetto takes his holograms as strip holograms in that both theholography and projection must be performed with the slit aperture. Thisrequires the holography of a very large number of small strip frames,the animation of each frame showing only slight or minuscule motion withrespect to the previous frame. This is contrasted with the method oftaking holographic movies where each frame has a reasonable size both inheight and in width (as would be expected in a standard format motionpicture film). Obviously, Dr. DeBitetto's technique has the disadvantageof requiring an extremely large number of frames, thus making theprocess very arduous. However, this patent application submits that theframes be prepared in the standard motion picture format (as opposed tohorizontal strip holograms), and that the frame be projected with ahorizontal slit aperture. The film is used in the same way as in Dr.DeBitetto's process, and is projected at constant velocity. The imageprojected from the hologram onto the screen will only change in verticalparallax as the frame moves by the aperture. However if the film formatused is that previously described for holography of the originaltwo-dimensional integral photographic film, then the vertical parallaxdoes not change as the frame moves by, because the projected image istwo-dimensional and has no vertical (nor horizontal) parallax. The imageonly changes, therefore, when a new frame comes into view. Therefore,the height of the frame required for the holographic film will dependupon the film velocity and the frame rate. This represents the preferredembodiment for the holographic projector.

Constant velocity is a tremendous advantage for projection ofthree-dimensional movies. Since film registration must be held toextremely tight tolerances, not having to stop the film for each framewould provide much needed stability, and film registration would be farsimpler. Without this constant velocity transport, each frame would haveto be registered with the three-point registration system as previouslydescribed. Furthermore, constant velocity film transport reduces theprobability of film breakage.

Primary projection of holographic films may be accomplished in the samemanner as it can for integral photographic films. In addition, theneeded magnification can be accomplished by direct projection. If theholographic film is produced using a plane reference wavefront, and anew holographic film is produced from it which is demagnified by a scalefactor “p”, then, when this new demagnified hologram is illuminated by aplane reference wavefront of the same wavelength, an image is producedwhich is magnified by the same scaling factor “p”. If the image of thehologram is a two-dimensional projected image of an integral photograph,primary projection is thus accomplished simply and without aberration.Image unmultiplexing, inversion and final projection are accomplished inthe same manner for holographic films as for integral photographicfilms.

The discussion now turns to intermediate processing of the film. In theprevious discussions of the formation of orthoscopic images frompseudoscopic images, image inversion was accomplished during theprojection stage. It is considered more desirable to accomplish thisoperation during the projection stage because it can be done without theinherent loss in resolution (a factor of {square root over (2)})attached to a process in which a new integral photograph or hologrammust be copied from the three-dimensional projected image. Should it bedesired to make a film to be presented to motion picture theaters,which, in turn, when projected, would produce orthoscopic images, thenthe best method of making such films from the original would be by theprojection techniques previously discussed. These projection techniquescan be used for film copying as well as for projection onto a screen.However, for the sake of completeness of this application, the methodsfor image inversion, by making a new integral photograph or hologramfrom the original reconstructed three-dimensional pseudoscopic image,will be presented.

FIGS. 65, 66 and 67 show the standard methods of performing thisinversion. FIG. 65 illustrates converting from one integral photographto another; FIG. 66, from an integral photograph to a hologram; and FIG.67, from one hologram to another. Note that, in each of these setups thefilm upon which the new integral photograph or hologram is to beproduced may be positioned anywhere with respect to the pseudoscopicimage. What is important is that the original reconstructed wavefrontsbe used to form the new record and not the image.

Another method (which is not current state-of-the-art) is shown in FIG.68. As was shown in FIG. 53 mirror inversion of each elementalphotograph in the integral photograph while keeping the original orderof the elemental photographs, will produce a film capable of projectingan orthoscopic image. This is accomplished by projecting each elementalphotograph onto a new record using a matrix lens array 203 as is shownin FIG. 68. Here both records, 204 and 205, are at a fixed distance sfrom the matrix lens array 203, determined by the principles ofprojection. Waveguides or baffles 206 are used to prevent overlapping ofthe images. However, there is much noise from the light scattered fromthe walls of the waveguides. Furthermore, while the resolution loss of{square root over (2)} is avoided in this case, there is a resolutionloss due to the fact that the two-dimensional images are projected.(This loss does not occur in the holographic projection techniquespreviously described.)

Another concept of this intermediate processing which would be extremelyuseful for reducing the most expensive parts of the projector, would beto place an unexposed film at the unscrambled image plane 154 of theprojector in FIG. 54. As the original integral photographic record isplayed through the projector, this new film is recording a newunmultiplexed pattern. This film, when used with a standard projectionlens can then project the required integral photograph onto the screen.

When performing intermediate processing on integral photographic films,it must be remembered that the integral photographic motion picture filmis produced on high resolution black & white film. Therefore, processingis simple and standard with one reservation. Care must be taken to avoidemulsion shrinkage. The exercise of proper care in processing can andwill avoid this problem.

There are two elements to be considered when processing holographicfilms. Holographic films produced photographically or by pressing.Photographically produced holograms are produced on extremely highresolution films, with a resolution approximating 2,000 lines/mm. Whileprocessing of these films is somewhat standard, extreme care must betaken to avoid emulsion shrinkage or dimensional changes in the film.Emulsion shrinkage during wet processing will not only cause distortionof the three-dimensional image, but also will cause changes in the colorproperties of the image.

It is feasible to process holograms in such a way as to avoid majordimensional changes in both the emulsion and the film. However, thisprocessing must be done with great care, and there is a statisticalprobability that some films will experience degradation. Yet, thisstatistical factor does not make wet processing of holographic filmsimpractical.

Another solution to the processing problem is to use materials that donot require wet processing. These materials will produce only phaseholograms. For surface holograms, thermoplastic and photochromicmaterials are available. For volume holograms, crystalline materials,such as lithium niobate (LiNbO₃), and certain optical cements areavailable. A 1 cc crystal of LiNbO₃ can store 1,000 holograms which aretemperature erasable. These holograms can be played back by angle tuningthe reference beam. Certain optical cements, developed at XEROX Corp.,are developable by ultraviolet radiation and have extremely highdiffraction efficiencies.

An extremely important method of obtaining consistently processed filmis to use a printing press arrangement to emboss a phase-only surfacehologram onto a plastic material. Once a metal plate is produced for aholographic frame or picture, holograms can be mass produced bothinexpensively and consistently. The reproduction process is identical torecord processing. Once the master is produced, millions of hologramscan be produced from the same original. After the processed hologram isproduced, it can be used directly as a high diffraction efficiency phasetransmission surface hologram or a metal can be vacuum deposited ontothe surface of the film, and the hologram can be used as a highdiffraction efficiency surface reflection hologram.

FIG. 69 illustrates the process for preparing the master. A laminatesuch as those used in the printed circuit industry is used as the basefor the master. This base consists of a metal (such as copper) laminatedto a plastic composite substrate (such as fiberglass impregnated withepoxy). A high resolution photoresist is coated onto the metal surface.This photoresist is the same as is used for the semiconductor industry.As is shown in FIG. 69(a), the hologram is then exposed onto thephotoresist using coherent illumination. This can either be done by astandard contact printing method or by direct holography. This exposurepolymerizes the photoresist only in those areas where exposure hasoccurred. In the second step, FIG. 69(b), the plate is placed into adeveloper, and the unpolymerized photoresist is dissolved away. Twoalternate processing techniques can be applied here. In the first method[see FIGS. 69(c) and (d)], metal can be plated onto the metal which wasexposed by dissolving the photoresist. After plating, the remainingundissolved polymerized photoresist can be removed chemically by apowerful stripper. This leaves a metal plate having surface contours inthe metal representative of the hologram. This plate can now be used asthe master for the printing process. In the second method [see FIGS.69(e) and (f)], the metal exposed by dissolving the photoresist isetched away chemically so as to expose the bottom substrate. Then theremaining photoresist is stripped away, and this plate can now be usedas the master.

The discussion now turns to the design of an editor for integralphotographs and holograms. Unfortunately, it is not practical to performediting on the reconstructed three-dimensional image, because it wouldrequire the building of yet another three-dimensional projector whichwould be very expensive. (Of course, editing can be done this way, butit is not too advisable.) However, it is very practical to project atwo-dimensional picture from the integral photographic or holographicfilms, and editing can be performed using these two-dimensional images.Other than the image projection mechanism, the editor design is quitestandard.

FIG. 70(a) shows how a two-dimensional image can be projected from anintegral photograph. A very small lens 207, such as a microscopeobjective, is used to project only one elemental photograph 208 of theintegral photograph 209 onto a translucent screen 210 with a very highmagnification. In FIG. 70(b), a laser 211 is used as shown to project atwo-dimensional real image 212 from a hologram 213 onto a translucentscreen 214. If the holographic film was produced by direct photographyof the three-dimensional image then this projected two-dimensional imagecan be used for editing. If the reconstructed image of the hologram is atwo-dimensional integral photograph, then this image can be projected toa two-dimensional elemental photographic image as is shown in FIG.65(a).

Finally, the application goes on to discuss alternate uses for thedevices, methods and processes presented herein. The thrust of thisapplication has been to show the utility of such a system for projectionof three-dimensional slides (still photography) and motion picturesbefore a large audience. The concepts of photography and projectionpresented herein, even though novel, seem to fall within the generalimpressions of what photography and projection are supposed to do. Nodiscussion has thus far been presented concerning uses of this systemfor television, computers, video taping and animation.

Broadcasting integral photographs over the airwaves for display andthree-dimensional reconstruction on standard NTSC television sets (orfor that matter, any display or 3-D rendering using the NTSC system) isunfeasible. The NTSC standard allows for 512 lines of resolution in thevertical direction. This resolution is insufficient for presentation ofthe amount of photographic information necessary for three-dimensionalreconstruction using the method of magnification and projectionpresented herein. Firstly, the conventional broadcasting bandwidth isinsufficient for transmission of the required information within thetime necessary to depict the correct number of motion picture frames forpersistence of vision. Secondly, no conventional television sets exist(including HD-TV) that possess the inherent resolution characteristicsfor this process. However, it is possible to construct a homeentertainment system (resembling a television set) that employs themethods and apparatus described in this application. Furthermore, whilebroadcasting of programming over conventional television broadcast bandsor even over conventional cable TV transmission is unfeasible due tobandwidth considerations, it is possible to adequately transmit imageinformation over closed circuit fiber optics cable. This hasimplications not only for home entertainment but also for computerdisplays. Using the methods and apparatus described herein, threedimensional computer graphics is feasible. Furthermore, the use ofmagnetic videotape (or other magnetic media) to record the informationnecessary for image retrieval using this method is also feasible. Soalso is the use of CD's of various formats (e.g., laser disc) feasiblefor this purpose.

It is now feasible to produce animated integral photographs capable ofproducing three-dimensional cartoons that can be subsequently magnifiedand projected before a large audience using the methods and apparatuspreviously described. Each frame of a motion picture (or a still lifeslide) consists of 1,730 individual elemental pictures. These elementalpictures depict the same scene but from slightly different viewpoints.In the past, animated cartoons were created by an artist drawingindividual frames, the difference between successive frames depictingthe passage of time. Usually the differences were in slight movement ofan object in the scene or of the viewpoint itself. For animated integralphotography, the artist can no longer draw only one frame for eachinstant of time, but he must draw 1,730 frames for the same instant. Inthe past, this would have added an incredible amount of labor to anartist's endeavors. However, with the aid of a computer, given thecurrent state of computer technology, these elemental pictures can bedrawn automatically. Therefore, one can expect to see cartoons as partof the repertoire of three-dimensional motion pictures.

While the preferred and alternate embodiments of the invention have beendescribed in detail, modifications may be made thereto, withoutdeparting from the spirit and scope of the invention as delineated inthe following claims:

What is claimed is:
 1. A method of preparing a hologram to be used in asystem for recording and projection of images in substantiallythree-dimensional format, said method comprising the steps of: producinga reference beam by passing diffuse coherent light from a laser througha first active optical system containing a plurality of image focusingmeans therein; and producing an object beam by passing diffuse coherentlight from said laser through a second active optical system containinga plurality of image focusing means therein of the same number andarrangement as the first active optical system, the F-number of eachsaid focusing means of the second active optical system being the sameas the F-number of the first active optical system, wherein all of thecomponent parts of an equation used for determining the F-number of thesecond optical system are substantially the same multiples of all of thecomponent parts used for determining the F-number of the first activeoptical system, respectively, said multiple being equal to the expectedmagnification of the three-dimensional image.